多元线性回归预测：餐馆营业额与多因素实战

<p style="text-align:center;"><strong style="letter-spacing:.544px;text-align:center;font-size:14px;"><img style="font-size:17px;letter-spacing:.544px;" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_png/y2fhgP4leThSFO11jUapfG5MmrJnqs1IiaBteLQbiaUvvS5Hy5HDxt7bp5CiayVTxxgw3gc5GaOLjOvmccGSDznog/640?wx_fmt=png" alt="640?wx_fmt=png"></strong></p><p style="min-height:1em;letter-spacing:.544px;border-width:0px;font-size:16px;vertical-align:baseline;font-family:'-apple-system', 'Helvetica Neue', Helvetica, 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', SimSun, 'Segoe UI', Roboto, sans-serif;"><span style="color:rgb(136,136,136);">作者：</span><strong style="color:rgb(136,136,136);">herain</strong><span style="color:rgb(136,136,136);">  R语言中文社区专栏作者</span><br></p><p style="min-height:1em;letter-spacing:.544px;border-width:0px;font-size:16px;vertical-align:baseline;font-family:'-apple-system', 'Helvetica Neue', Helvetica, 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', SimSun, 'Segoe UI', Roboto, sans-serif;"><span style="color:rgb(136,136,136);">知乎ID：https://www.zhihu.com/people/herain-14</span></p><p style="min-height:1em;letter-spacing:.544px;line-height:27.2px;"><span style="font-size:16px;"><strong style="letter-spacing:.544px;"><br></strong></span></p><p style="min-height:1em;letter-spacing:.544px;line-height:27.2px;"><span style="font-size:16px;"><strong style="letter-spacing:.544px;">前言</strong></span></p><p><a href="http://mp.weixin.qq.com/s?__biz=MzA3MTM3NTA5Ng==&mid=2651060000&idx=1&sn=0f3ede69c91eb7df503a3ea6407be882&chksm=84d9d6b7b3ae5fa1b461c25f9c5aaad44b8f8639df356471e3741a3fd8a044de7b822e72c7ed&scene=21#wechat_redirect" rel="nofollow" style="font-size:16px;text-decoration:underline;" target="_blank"><span style="font-size:16px;">上篇</span></a><span style="font-size:16px;"><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;">我们用一元线性回归预测</span><span style="font-size:16px;letter-spacing:.544px;text-align:justify;">销售收入与广告支出实战，但</span>世界是复杂的，有因有果，因果迭交，我们常说事或物是多种因素共同作用的结果，今天我们从统计学角度，去分析多种因素是怎么样作用一种事物，产生不一样的结果。</span></p><p><br></p><span style="color:rgb(255,255,255);font-size:16px;"><strong>综述</strong></span><p style="min-height:1em;letter-spacing:.544px;"><span style="font-size:16px;color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;">以餐馆营业额作为果（y= 日均营业额/万元），周边居民人数（x1 /万人），用餐平均支出（x2 / 元/人），周边居民月平均收入（x3/ 元），周边餐馆数（x4/ 个），距市中心距离（x5/ km）作为因素，来探索因与果之间的回归模型，发现规律，改善餐馆营销方式，提高餐馆的营业额。<br></span></p><p style="min-height:1em;letter-spacing:.544px;"><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;"><br></span></p><span style="color:rgb(255,255,255);font-size:16px;"><strong>分析步骤</strong></span><h2><span style="font-size:16px;"><strong>餐馆营业额与多因素的回归模型分析步骤：</strong></span></h2><p style="text-align:left;"><span style="font-size:16px;">1.确定所关注的因变量y 和影响因变量的k个自变量</span></p><p style="text-align:left;"><span style="font-size:16px;">2.假定因变量y 与 k 个自变量之间为线性关系，并建立线性关系模型</span></p><p style="text-align:left;"><span style="font-size:16px;">3.对模型进行估计和检验</span></p><p style="text-align:left;"><span style="font-size:16px;">4.判别模型中是否存在多重共线性，如果存在，进行处理</span></p><p style="text-align:left;"><span style="font-size:16px;">5.利用回归方程进行预测</span></p><p style="text-align:left;"><span style="font-size:16px;">6.对回归模型进行诊断</span></p><p style="min-height:1em;letter-spacing:.544px;"><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;"><br></span></p><span style="color:rgb(255,255,255);font-size:16px;"><strong>1 确定因变量y和影响因变量的k个自变量</strong></span><p><span style="font-weight:600;font-size:16px;">1.1 </span><span style="font-size:16px;"><strong>确定因变量和自变量</strong></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;"><span style="font-size:16px;font-weight:600;">y:餐馆营业额作为果</span>（y= 日均营业额/万元）</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;"><strong>k个自变量为：</strong></span></p><ul class="list-paddingleft-2" style="list-style-type:disc;"><li><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">周边居民人数（x1 /万人）</span></p></li><li><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">用餐平均支出（x2 / 元/人）</span></p></li><li><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">周边居民月平均收入（x3/ 元）</span></p></li><li><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">周边餐馆数（x4/ 个）</span></p></li><li><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">距市中心距离（x5/ km）</span></p></li></ul><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><p><span style="font-weight:600;font-size:16px;">1.2 </span><span style="font-size:16px;"><strong>分析的数据：</strong></span></p><blockquote><pre style="font-size:.9em;"><code class="language-text" style="font-family:Menlo, Monaco, Consolas, 'Andale Mono', 'lucida console', 'Courier New', monospace;font-size:inherit;"><span style="font-size:16px;">   index    y    x1    x2    x3 x4   x5
1      1 53.2 163.0 168.6  6004  5  6.5
2      2 18.5  14.5  22.5   209 11 16.0
3      3 11.3  88.2 109.4  1919 10 18.2
4      4 84.7 151.6 277.0  7287  7 10.0
5      5  7.3  79.1  17.4  5311 15 17.5
6      6 17.9  60.4  93.0  6109  8  3.6
7      7  2.5  53.2  21.5  4057 17 18.5
8      8 27.3 108.5 114.5  4161  3  4.0
9      9  5.9  48.7  61.3  2166 10 11.6
10    10 23.9 142.8 129.8 11125  9 14.2
11    11 69.4 214.7 159.4 13937  2  2.5
12    12 20.6  65.6  91.0  4000 18 12.0
13    13  1.9  13.2   6.1  2841 14 12.8
14    14  3.0  60.9  60.3  1273 26  7.8
15    15  7.3  21.2  51.1  2404 34  2.7
16    16 46.2 114.3  73.6  6109 12  3.2
17    17 78.8 299.5 171.7 15571  4  7.6
18    18 11.1  78.9  38.8  4228 11 11.0
19    19  8.6  90.0 105.3  3772 15 28.4
20    20 48.9 160.3 161.5  6451  5  6.2
21    21 22.1  84.0 122.6  3275  9 10.8
22    22 11.1  78.9  38.8  4228 10 33.7
23    23  8.6  90.0 105.3  3772 14 16.5
24    24 48.9 160.3 161.5  6451  6  9.3
25    25 22.1  84.0 122.6  3275 10 11.6</span></code></pre></blockquote><p><br></p><span style="color:rgb(255,255,255);font-size:15px;"><strong>2 建立线性关系模型</strong></span><p><strong><span style="font-size:16px;">公式：</span></strong></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="1028" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHUgiaNibHYcbK4uLI7ibIcFedc1JWKX1ib6aVib2NxNWBuLEJwUZwibkia1F2w/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">2.1 </span><span style="font-size:16px;"><strong>绘制多个变量的相关图：</strong></span></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs vbnet"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;">> library(corrgram)</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> corrgram(example10_1[<span class="hljs-number">2</span>:<span class="hljs-number">7</span>], <span class="hljs-keyword">order</span>=T, lower.panel=panel.shade,upper.panel=panel.pie,<span class="hljs-keyword">text</span>=panel.txt)</div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><br></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="1196" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHWribpXX2tXM8Qzib6Hv0lAib2Y6fjVOpVvuf8ibGdZNdp3SehSYbAe70Mg/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"><figcaption style="font-size:.9em;line-height:1.5;text-align:center;color:rgb(153,153,153);"><span style="font-size:16px;">6个变量之间的相关图（相关系数矩阵图）</span></figcaption></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">解读相关系数矩阵图，请参考搜索，获取了解。蓝色表示正相关，红色表示负相关，对应颜色的饼图表示相关的度。</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">2.2 </span><span style="font-size:16px;"><strong>建立回归模型（检测报告，模型进行估计和检验用到了如下检测结果）：</strong></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">检测报告：</span></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs vbnet"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;"><span class="hljs-meta">#回归模型拟合</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> fit1 <- lm(y~x1+x2+x3+x4+x5, data=example10_1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> summary(fit1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-keyword">Call</span>:</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">lm(formula = y ~ x1 + x2 + x3 + x4 + x5, data = example10_1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Residuals:</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">     Min       <span class="hljs-number">1</span>Q   Median       <span class="hljs-number">3</span>Q      Max </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">-16.7204</span>  <span class="hljs-number">-6.0600</span>   <span class="hljs-number">0.7152</span>   <span class="hljs-number">3.2144</span>  <span class="hljs-number">21.4805</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Coefficients:</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">              Estimate Std. <span class="hljs-keyword">Error</span> t value Pr(>|t|)   </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">(Intercept)  <span class="hljs-number">4.2604768</span> <span class="hljs-number">10.4679833</span>   <span class="hljs-number">0.407</span>  <span class="hljs-number">0.68856</span>   </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1           <span class="hljs-number">0.1273254</span>  <span class="hljs-number">0.0959790</span>   <span class="hljs-number">1.327</span>  <span class="hljs-number">0.20037</span>   </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2           <span class="hljs-number">0.1605660</span>  <span class="hljs-number">0.0556834</span>   <span class="hljs-number">2.884</span>  <span class="hljs-number">0.00952</span> **</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x3           <span class="hljs-number">0.0007636</span>  <span class="hljs-number">0.0013556</span>   <span class="hljs-number">0.563</span>  <span class="hljs-number">0.57982</span>   </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="18"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x4          <span class="hljs-number">-0.3331990</span>  <span class="hljs-number">0.3986248</span>  <span class="hljs-number">-0.836</span>  <span class="hljs-number">0.41362</span>   </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="19"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5          <span class="hljs-number">-0.5746462</span>  <span class="hljs-number">0.3087506</span>  <span class="hljs-number">-1.861</span>  <span class="hljs-number">0.07826</span> . </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="20"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">---</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="21"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Signif. codes:  <span class="hljs-number">0</span> ‘***’ <span class="hljs-number">0.001</span> ‘**’ <span class="hljs-number">0.01</span> ‘*’ <span class="hljs-number">0.05</span> ‘.’ <span class="hljs-number">0.1</span> ‘ ’ <span class="hljs-number">1</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="22"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="23"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Residual standard <span class="hljs-keyword">error</span>: <span class="hljs-number">10.65</span> <span class="hljs-keyword">on</span> <span class="hljs-number">19</span> degrees <span class="hljs-keyword">of</span> freedom</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="24"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Multiple R-squared:  <span class="hljs-number">0.8518</span>,    Adjusted R-squared:  <span class="hljs-number">0.8128</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="25"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">F-statistic: <span class="hljs-number">21.84</span> <span class="hljs-keyword">on</span> <span class="hljs-number">5</span> <span class="hljs-keyword">and</span> <span class="hljs-number">19</span> DF,  p-value: <span class="hljs-number">2.835e-07</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="26"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="27"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#计算回归系数的置信区间</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="28"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> confint(fit1, level=<span class="hljs-number">0.95</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="29"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">                    <span class="hljs-number">2.5</span> %       <span class="hljs-number">97.5</span> %</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="30"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">(Intercept) <span class="hljs-number">-17.649264072</span> <span class="hljs-number">26.170217667</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="31"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1           <span class="hljs-number">-0.073561002</span>  <span class="hljs-number">0.328211809</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="32"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2            <span class="hljs-number">0.044019355</span>  <span class="hljs-number">0.277112598</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="33"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x3           <span class="hljs-number">-0.002073719</span>  <span class="hljs-number">0.003600932</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="34"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x4           <span class="hljs-number">-1.167530271</span>  <span class="hljs-number">0.501132297</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="35"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5           <span class="hljs-number">-1.220868586</span>  <span class="hljs-number">0.071576251</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="36"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="37"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#输出方差分析表</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="38"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> anova(fit1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="39"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Analysis <span class="hljs-keyword">of</span> Variance Table</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="40"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="41"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Response: y</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="42"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">          Df  Sum Sq Mean Sq F value    Pr(>F)    </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="43"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1         <span class="hljs-number">1</span> <span class="hljs-number">10508.9</span> <span class="hljs-number">10508.9</span> <span class="hljs-number">92.7389</span> <span class="hljs-number">9.625e-09</span> ***</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="44"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2         <span class="hljs-number">1</span>  <span class="hljs-number">1347.1</span>  <span class="hljs-number">1347.1</span> <span class="hljs-number">11.8878</span>  <span class="hljs-number">0.002696</span> ** </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="45"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x3         <span class="hljs-number">1</span>    <span class="hljs-number">85.4</span>    <span class="hljs-number">85.4</span>  <span class="hljs-number">0.7539</span>  <span class="hljs-number">0.396074</span>    </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="46"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x4         <span class="hljs-number">1</span>    <span class="hljs-number">40.5</span>    <span class="hljs-number">40.5</span>  <span class="hljs-number">0.3573</span>  <span class="hljs-number">0.557082</span>    </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="47"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5         <span class="hljs-number">1</span>   <span class="hljs-number">392.5</span>   <span class="hljs-number">392.5</span>  <span class="hljs-number">3.4641</span>  <span class="hljs-number">0.078262</span> .  </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="48"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Residuals <span class="hljs-number">19</span>  <span class="hljs-number">2153.0</span>   <span class="hljs-number">113.3</span>                      </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="49"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">---</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="50"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Signif. codes:  <span class="hljs-number">0</span> ‘***’ <span class="hljs-number">0.001</span> ‘**’ <span class="hljs-number">0.01</span> ‘*’ <span class="hljs-number">0.05</span> ‘.’ <span class="hljs-number">0.1</span> ‘ ’ <span class="hljs-number">1</span></div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><br></p><p><span style="font-size:16px;"><span style="font-family:'宋体';">从检验结果可以看出</span> x1<span style="font-family:'宋体';">，</span>x2<span style="font-family:'宋体';">，</span>x5 <span style="font-family:'宋体';">对</span> y <span style="font-family:'宋体';">的总误差平方和贡献显著。</span></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;"><br></span></p><p><strong><span style="font-size:16px;">2.3 回归模型方程式：</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">计算：y = 4.2604768 + 0.1273254*x1 + 0.1605660*x2 + 0.0007636x3 -0.3331990 x4 -0.5746462 * x5</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><span style="color:rgb(255,255,255);font-size:16px;"><strong>3 对模型进行估计和检验</strong></span><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">3.1 </span><strong><span style="font-size:16px;">拟合优度检验</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">多重决定系数是多元线性回归中回归平方和SSR 占总平方和SST的比例，计算公式为：</span></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="658" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcH1qhvESWj7JcbcBibhtPRlb7PiaFMdHJvZJ86gfzpoSua3RkH1xd1SBrg/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">它表示因变量y的总误差中被多少个自变量共同解释的比例。</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">为避免增加自变量而高估多重决定系数，统计学家使用样本量n和自变量的个数k 去调整 <span style="font-size:16px;font-weight:600;">多重决定系数：</span></span></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="714" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHAM6ibbUuo3rnMHibPTYIYUkEFRaiayibsMHdmjDHrk0qfBxsrZLsSqXRkw/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">计算知：多重决定系数为：0.8518，说明日均营业额时与周边居民人数，用餐平均支出，周边居民月平均收入，周边餐馆数和距离市中心这5个自变量模型的拟合度较高。</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">Multiple R-squared: 0.8518,   Adjusted R-squared: 0.8128</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">3.2 </span><strong><span style="font-size:16px;">估计标准误：</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">标准误就是指残差的标准差，计算公式：</span></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="850" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHREr2hQrLEXjtfcCib1UoYktV8S7eCz20kD6NU23ibRsYCxvRUouokd9w/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">计算知：估计的标准误差为：10.65，根据建立的多元线性回归方程，周边居民人数，用餐平均支出，周边居民月平均收入，周边餐馆数和距离市中心这5个自变量预测日均营业额时，平均的预测误差为10.65万元<br><br>Residual standard error: 10.65 on 19 degrees of freedom<br></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;"><br></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">3.3 </span><strong><span style="font-size:16px;">模型的显著性检验</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">包含如下检验：线性关系检验，回归系数检验。请参考（2.2处：检测报告）诠释如下两种假设，此次省略具体说明。</span></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="712" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHSgOh6SE3XbYLNTJW6smj0qEQZAxVwkqcWfqCIsrHWjRJrIzA4kvialg/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="732" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHVHojL5xFXWMIbC38Fyu7YKN8syZ2vHFHD5AZIHVJgHuicPL2xYzFhGQ/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">3.4 </span><strong><span style="font-size:16px;">模型诊断</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">绘制残差图诊断模型</span></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs swift"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;">> par(mfrow=<span class="hljs-built_in">c</span>(<span class="hljs-number">1</span>,<span class="hljs-number">2</span>), mai=<span class="hljs-built_in">c</span>(<span class="hljs-number">0.8</span>,<span class="hljs-number">0.8</span>,<span class="hljs-number">0.4</span>,<span class="hljs-number">0.1</span>),cex=<span class="hljs-number">0.8</span>,cex.main=<span class="hljs-number">0.7</span>)</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> plot(fit1,which=<span class="hljs-number">1</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> plot(fit1,which=<span class="hljs-number">2</span>)</div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><br></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="1200" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHbPqKaibblib9Viau2ClFGIicGny8FMMxTO0Ye0BnoVPic7DPkEWE6ypicW7w/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"><figcaption style="font-size:.9em;line-height:1.5;text-align:center;color:rgb(153,153,153);"><span style="font-size:16px;">残差图</span></figcaption></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">在图中发现点2，4，16具有较大残差，残差的正态性存在问题（可以考虑重建模型，或者剔除较大残差值），如下我们剔除点 2，4 重新建立回归模型：</span></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs bash"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;"><span class="hljs-comment">#再次绘制残差图</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> par(mfrow=c(1,2), mai=c(0.8,0.8,0.4,0.1),cex=0.8,cex.main=0.7)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> plot(newfit1,<span class="hljs-built_in">which</span>=1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> plot(newfit1,<span class="hljs-built_in">which</span>=2)</div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><br></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="1200" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcH1pp6rO6vcvom0eU1AoOfkWNvBHo9RIr2IIRm2ialqSia6CF5P4K0gfBA/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"><figcaption style="font-size:.9em;line-height:1.5;text-align:center;color:rgb(153,153,153);"><span style="font-size:16px;">去掉点2，4的残差图</span></figcaption></figure><span style="color:rgb(255,255,255);font-size:16px;"><strong>4 判别模型中是否存在多重共线性</strong></span><p style="min-height:1em;letter-spacing:.544px;"><span style="font-weight:600;color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;">4.1 </span><strong><span style="font-size:16px;">判别的重要性</span></strong></p><p><span style="font-size:16px;">变量之间的高度相关性，造成回归结果的混乱。多重共性性可能对参数估计值的正负号产生影响。<br></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">4.2 </span><strong><span style="font-size:16px;">识别共线性和处理</span></strong></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs vbnet"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;"><span class="hljs-meta">#1，自变量之间的相关系数及其检验</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> library(psych)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> corr.test(example10_1[<span class="hljs-number">3</span>:<span class="hljs-number">7</span>], use=<span class="hljs-string">"complete"</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-keyword">Call</span>:corr.test(x = example10_1[<span class="hljs-number">3</span>:<span class="hljs-number">7</span>], use = <span class="hljs-string">"complete"</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Correlation matrix </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  x1x2x3x4x5</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1  <span class="hljs-number">1.00</span>  <span class="hljs-number">0.74</span>  <span class="hljs-number">0.88</span> <span class="hljs-number">-0.62</span> <span class="hljs-number">-0.28</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2  <span class="hljs-number">0.74</span>  <span class="hljs-number">1.00</span>  <span class="hljs-number">0.55</span> <span class="hljs-number">-0.54</span> <span class="hljs-number">-0.32</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x3  <span class="hljs-number">0.88</span>  <span class="hljs-number">0.55</span>  <span class="hljs-number">1.00</span> <span class="hljs-number">-0.52</span> <span class="hljs-number">-0.29</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x4 <span class="hljs-number">-0.62</span> <span class="hljs-number">-0.54</span> <span class="hljs-number">-0.52</span>  <span class="hljs-number">1.00</span>  <span class="hljs-number">0.10</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5 <span class="hljs-number">-0.28</span> <span class="hljs-number">-0.32</span> <span class="hljs-number">-0.29</span>  <span class="hljs-number">0.10</span>  <span class="hljs-number">1.00</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Sample Size </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">[<span class="hljs-number">1</span>] <span class="hljs-number">25</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Probability values (Entries above the diagonal are adjusted <span class="hljs-keyword">for</span> multiple tests.) </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> x1   x2   x3   x4   x5</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1 <span class="hljs-number">0.00</span> <span class="hljs-number">0.00</span> <span class="hljs-number">0.00</span> <span class="hljs-number">0.01</span> <span class="hljs-number">0.47</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2 <span class="hljs-number">0.00</span> <span class="hljs-number">0.00</span> <span class="hljs-number">0.03</span> <span class="hljs-number">0.03</span> <span class="hljs-number">0.46</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="18"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x3 <span class="hljs-number">0.00</span> <span class="hljs-number">0.00</span> <span class="hljs-number">0.00</span> <span class="hljs-number">0.04</span> <span class="hljs-number">0.47</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="19"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x4 <span class="hljs-number">0.00</span> <span class="hljs-number">0.01</span> <span class="hljs-number">0.01</span> <span class="hljs-number">0.00</span> <span class="hljs-number">0.65</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="20"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5 <span class="hljs-number">0.18</span> <span class="hljs-number">0.12</span> <span class="hljs-number">0.16</span> <span class="hljs-number">0.65</span> <span class="hljs-number">0.00</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="21"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="22"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-keyword">To</span> see confidence intervals <span class="hljs-keyword">of</span> the correlations, print <span class="hljs-keyword">with</span> the <span class="hljs-built_in">short</span>=<span class="hljs-literal">FALSE</span> <span class="hljs-keyword">option</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="23"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="24"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#2，考察回归系数的显著性</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="25"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#3，分析回归系数的正负号</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="26"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#4，用容忍度和方差膨胀因子（VIF）,VIF 大于10 存在严重的共线性:</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="27"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> library(car)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="28"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">载入需要的程辑包：carData</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="29"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">载入程辑包：‘car’</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="30"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">The following <span class="hljs-built_in">object</span> <span class="hljs-keyword">is</span> masked <span class="hljs-keyword">from</span> ‘package:psych’:logit</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="31"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="32"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> library(carData)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="33"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> vif(fit1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="34"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  x1   x2   x3   x4   x5 </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="35"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">8.233159</span> <span class="hljs-number">2.629940</span> <span class="hljs-number">5.184365</span> <span class="hljs-number">1.702361</span> <span class="hljs-number">1.174053</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="36"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> <span class="hljs-number">1</span>/vif(fit1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="37"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">   x1x2x3x4x5 </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="38"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">0.1214601</span> <span class="hljs-number">0.3802368</span> <span class="hljs-number">0.1928877</span> <span class="hljs-number">0.5874195</span> <span class="hljs-number">0.8517500</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="39"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> </div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">如上分析数据可知，不存在严重的共线性问题</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><br></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">4.3 </span><strong><span style="font-size:16px;">变量的选择与逐步回归</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">建立模型之前就有选择的确定进入模型的自变量，也可以避免多重共线性问题，变量的选择方法主要有 </span><strong><span style="font-size:16px;">向前选择，向后剔除，逐步回归</span></strong><span style="font-size:16px;"><span style="font-size:16px;font-weight:600;"> </span>等。</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">逐步回归以赤池信息准则AIC为选择标准，选择AIC最小的变量建立模型，计算公式为：</span></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="598" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHkm2GgVkr8Rt2k1RDSiaQ5BFkfQicuibBG8icxukLwIEN76Oic88CQVJznHA/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">式中，n为样本量；p为模型中参数的个数（包括常数项）</span></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs vbnet"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;"><span class="hljs-meta">#对模型fit1进行逐步回归</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> fit2 <-<span class="hljs-keyword">step</span>(fit1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Start:  AIC=<span class="hljs-number">123.39</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">y ~ x1 + x2 + x3 + x4 + x5</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">       Df Sum <span class="hljs-keyword">of</span> Sq    RSS    AIC</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x3    <span class="hljs-number">1</span>     <span class="hljs-number">35.96</span> <span class="hljs-number">2189.0</span> <span class="hljs-number">121.81</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x4    <span class="hljs-number">1</span>     <span class="hljs-number">79.17</span> <span class="hljs-number">2232.2</span> <span class="hljs-number">122.30</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><none>              <span class="hljs-number">2153.0</span> <span class="hljs-number">123.39</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x1    <span class="hljs-number">1</span>    <span class="hljs-number">199.42</span> <span class="hljs-number">2352.4</span> <span class="hljs-number">123.61</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x5    <span class="hljs-number">1</span>    <span class="hljs-number">392.54</span> <span class="hljs-number">2545.6</span> <span class="hljs-number">125.58</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x2    <span class="hljs-number">1</span>    <span class="hljs-number">942.22</span> <span class="hljs-number">3095.2</span> <span class="hljs-number">130.47</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-keyword">Step</span>:  AIC=<span class="hljs-number">121.81</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">y ~ x1 + x2 + x4 + x5</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">       Df Sum <span class="hljs-keyword">of</span> Sq    RSS    AIC</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="18"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x4    <span class="hljs-number">1</span>     <span class="hljs-number">78.22</span> <span class="hljs-number">2267.2</span> <span class="hljs-number">120.69</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="19"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><none>              <span class="hljs-number">2189.0</span> <span class="hljs-number">121.81</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="20"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x5    <span class="hljs-number">1</span>    <span class="hljs-number">445.69</span> <span class="hljs-number">2634.7</span> <span class="hljs-number">124.44</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="21"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x2    <span class="hljs-number">1</span>    <span class="hljs-number">925.88</span> <span class="hljs-number">3114.9</span> <span class="hljs-number">128.63</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="22"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x1    <span class="hljs-number">1</span>   <span class="hljs-number">1133.27</span> <span class="hljs-number">3322.3</span> <span class="hljs-number">130.24</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="23"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="24"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-keyword">Step</span>:  AIC=<span class="hljs-number">120.69</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="25"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">y ~ x1 + x2 + x5</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="26"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="27"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">       Df Sum <span class="hljs-keyword">of</span> Sq    RSS    AIC</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="28"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><none>              <span class="hljs-number">2267.2</span> <span class="hljs-number">120.69</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="29"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x5    <span class="hljs-number">1</span>    <span class="hljs-number">404.28</span> <span class="hljs-number">2671.5</span> <span class="hljs-number">122.79</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="30"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x2    <span class="hljs-number">1</span>   <span class="hljs-number">1050.90</span> <span class="hljs-number">3318.1</span> <span class="hljs-number">128.21</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="31"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">- x1    <span class="hljs-number">1</span>   <span class="hljs-number">1661.83</span> <span class="hljs-number">3929.0</span> <span class="hljs-number">132.43</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="32"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="33"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="34"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> fit2 <- lm(y~x1+x2+x5, data=example10_1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="35"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> summary(fit2)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="36"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="37"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-keyword">Call</span>:</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="38"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">lm(formula = y ~ x1 + x2 + x5, data = example10_1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="39"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="40"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Residuals:</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="41"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">    Min      <span class="hljs-number">1</span>Q  Median      <span class="hljs-number">3</span>Q     Max </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="42"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">-14.027</span>  <span class="hljs-number">-5.361</span>  <span class="hljs-number">-1.560</span>   <span class="hljs-number">2.304</span>  <span class="hljs-number">23.001</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="43"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="44"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Coefficients:</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="45"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">            Estimate Std. <span class="hljs-keyword">Error</span> t value Pr(>|t|)    </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="46"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">(Intercept) <span class="hljs-number">-1.68928</span>    <span class="hljs-number">6.25242</span>  <span class="hljs-number">-0.270</span>  <span class="hljs-number">0.78966</span>    </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="47"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1           <span class="hljs-number">0.19022</span>    <span class="hljs-number">0.04848</span>   <span class="hljs-number">3.923</span>  <span class="hljs-number">0.00078</span> ***</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="48"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2           <span class="hljs-number">0.15763</span>    <span class="hljs-number">0.05052</span>   <span class="hljs-number">3.120</span>  <span class="hljs-number">0.00518</span> ** </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="49"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5          <span class="hljs-number">-0.56979</span>    <span class="hljs-number">0.29445</span>  <span class="hljs-number">-1.935</span>  <span class="hljs-number">0.06656</span> .  </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="50"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">---</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="51"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Signif. codes:  <span class="hljs-number">0</span> ‘***’ <span class="hljs-number">0.001</span> ‘**’ <span class="hljs-number">0.01</span> ‘*’ <span class="hljs-number">0.05</span> ‘.’ <span class="hljs-number">0.1</span> ‘ ’ <span class="hljs-number">1</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="52"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="53"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Residual standard <span class="hljs-keyword">error</span>: <span class="hljs-number">10.39</span> <span class="hljs-keyword">on</span> <span class="hljs-number">21</span> degrees <span class="hljs-keyword">of</span> freedom</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="54"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Multiple R-squared:  <span class="hljs-number">0.8439</span>,    Adjusted R-squared:  <span class="hljs-number">0.8216</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="55"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">F-statistic: <span class="hljs-number">37.85</span> <span class="hljs-keyword">on</span> <span class="hljs-number">3</span> <span class="hljs-keyword">and</span> <span class="hljs-number">21</span> DF,  p-value: <span class="hljs-number">1.187e-08</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="56"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="57"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="58"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-meta">#逐步回归的方差分析</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="59"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> anova(fit2)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="60"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Analysis <span class="hljs-keyword">of</span> Variance Table</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="61"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="62"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Response: y</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="63"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">          Df  Sum Sq Mean Sq F value    Pr(>F)    </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="64"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x1         <span class="hljs-number">1</span> <span class="hljs-number">10508.9</span> <span class="hljs-number">10508.9</span> <span class="hljs-number">97.3392</span> <span class="hljs-number">2.452e-09</span> ***</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="65"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x2         <span class="hljs-number">1</span>  <span class="hljs-number">1347.1</span>  <span class="hljs-number">1347.1</span> <span class="hljs-number">12.4775</span>  <span class="hljs-number">0.001976</span> ** </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="66"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">x5         <span class="hljs-number">1</span>   <span class="hljs-number">404.3</span>   <span class="hljs-number">404.3</span>  <span class="hljs-number">3.7447</span>  <span class="hljs-number">0.066558</span> .  </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="67"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Residuals <span class="hljs-number">21</span>  <span class="hljs-number">2267.2</span>   <span class="hljs-number">108.0</span>                      </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="68"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">---</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="69"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">Signif. codes:  <span class="hljs-number">0</span> ‘***’ <span class="hljs-number">0.001</span> ‘**’ <span class="hljs-number">0.01</span> ‘*’ <span class="hljs-number">0.05</span> ‘.’ <span class="hljs-number">0.1</span> ‘ ’ <span class="hljs-number">1</span></div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><br></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">根据R的逐步回归结果，得到最终的估计方程：</span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><strong><span style="font-size:16px;">y = -1.68928 + 0.19022 * x1 + 0.15763 * x2 - 0.56979 * x3</span></strong></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs bash"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;">> par(mfcol=c(1,2),cex=0.7)</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> plot(fit2, <span class="hljs-built_in">which</span>=1)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> plot(fit2,<span class="hljs-built_in">which</span>=2)</div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><br></p><figure style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><img class="origin_image zh-lightbox-thumb lazy" style="margin-left:auto;" width="1200" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leTgbxgib1OpxiakdVlEobwBIcHpgknWAhjsuibicziakcUrqM5JHcJA20qsFaftt2EPIJUsMxGnuaBn7sicw/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"><figcaption style="font-size:.9em;line-height:1.5;text-align:center;color:rgb(153,153,153);"><span style="font-size:16px;">逐步回归模型的诊断图</span></figcaption></figure><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;"><br></span></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-weight:600;font-size:16px;">4.4 </span><strong><span style="font-size:16px;">多模型的比较</span></strong></p><p style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:medium;"><span style="font-size:16px;">完全模型，简化模型</span></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs css"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;">#模型方差对比</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> <span class="hljs-selector-tag">anova</span>(<span class="hljs-selector-tag">fit1</span>, <span class="hljs-selector-tag">fit2</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-selector-tag">Analysis</span> <span class="hljs-selector-tag">of</span> <span class="hljs-selector-tag">Variance</span> <span class="hljs-selector-tag">Table</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-selector-tag">Model</span> 1: <span class="hljs-selector-tag">y</span> ~ <span class="hljs-selector-tag">x1</span> + <span class="hljs-selector-tag">x2</span> + <span class="hljs-selector-tag">x3</span> + <span class="hljs-selector-tag">x4</span> + <span class="hljs-selector-tag">x5</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-selector-tag">Model</span> 2: <span class="hljs-selector-tag">y</span> ~ <span class="hljs-selector-tag">x1</span> + <span class="hljs-selector-tag">x2</span> + <span class="hljs-selector-tag">x5</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  <span class="hljs-selector-tag">Res</span><span class="hljs-selector-class">.Df</span>    <span class="hljs-selector-tag">RSS</span> <span class="hljs-selector-tag">Df</span> <span class="hljs-selector-tag">Sum</span> <span class="hljs-selector-tag">of</span> <span class="hljs-selector-tag">Sq</span>      <span class="hljs-selector-tag">F</span> <span class="hljs-selector-tag">Pr</span>(><span class="hljs-selector-tag">F</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">1     19 2153<span class="hljs-selector-class">.0</span>                           </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">2     21 2267<span class="hljs-selector-class">.2</span> <span class="hljs-selector-tag">-2</span>   <span class="hljs-selector-tag">-114</span><span class="hljs-selector-class">.17</span> 0<span class="hljs-selector-class">.5038</span> 0<span class="hljs-selector-class">.6121</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">#机器的交叉验证</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">#五折交叉验证</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-selector-id">#AIC</span>对比</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> <span class="hljs-selector-tag">AIC</span>(<span class="hljs-selector-tag">fit1</span>, <span class="hljs-selector-tag">fit2</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">     <span class="hljs-selector-tag">df</span>      <span class="hljs-selector-tag">AIC</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-selector-tag">fit1</span>  7 196<span class="hljs-selector-class">.3408</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-selector-tag">fit2</span>  5 193<span class="hljs-selector-class">.6325</span></div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;"><br></span></p><p><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;">对比数据，得知 fit2 模型的拟合的更好。</span></p><p><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;"><br></span></p><span style="color:rgb(255,255,255);font-size:16px;"><strong>5 利用回归方程进行预测</strong></span><p style="min-height:1em;letter-spacing:.544px;"><strong><span style="font-size:16px;">基于多点的点估计，求出区间估计（均值的区间估计，个别值的预测区间）</span></strong></p><p style="min-height:1em;letter-spacing:.544px;"><strong><span style="font-size:16px;"><br></span></strong></p><pre style="margin-left:0px;border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;font-size:13px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:solid;border-right-style:solid;border-bottom-style:solid;border-left-style:solid;border-top-color:rgb(204,204,204);border-right-color:rgb(204,204,204);border-bottom-color:rgb(204,204,204);border-left-color:rgb(204,204,204);line-height:19px;" onclick="hljs.copyCode(event)"><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs xml"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;">#计算置信区间和预测区间</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> x<span class="hljs-tag"><span class="hljs-tag"><<span class="hljs-name">-</span> <span class="hljs-attr">example10_1</span>[,<span class="hljs-attr">c</span>(<span class="hljs-attr">3</span>,<span class="hljs-attr">4</span>,<span class="hljs-attr">7</span>)]</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-tag">></span> pre<span class="hljs-tag"><<span class="hljs-name">-predict(fit2)</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> res<span class="hljs-tag"><<span class="hljs-name">-residuals(fit2)</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> zre<span class="hljs-tag"><<span class="hljs-name">-rstandard(fit2)</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> con_int<span class="hljs-tag"><<span class="hljs-name">-predict(fit2,x,interval="confidence",level=0.95)</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> pre_int<span class="hljs-tag"><<span class="hljs-name">-predict(fit2,x,interval="prediction",level=0.95)</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> mysummary<span class="hljs-tag"><<span class="hljs-name">-data.frame(日均营业额=example10_1$y,</span> 点预测值=<span class="hljs-string">pre,残差</span>=<span class="hljs-string">res,标准化残差</span>=<span class="hljs-string">zre,</span> </span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">置信下限=<span class="hljs-string">con_int[,2],</span> 置信上限=<span class="hljs-string">con_int[,3],</span> 预测下限=<span class="hljs-string">pre_int[,2],</span> 预测上限=<span class="hljs-string">pre_int[,3])</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> round(mysummary,3)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">   日均营业额点预测值残差标准化残差置信下限置信上限预测下限预测上限</div></div></li></ol></code><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs css"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:14px;">153<span class="hljs-selector-class">.2</span>   52<span class="hljs-selector-class">.189</span>   1<span class="hljs-selector-class">.011</span>  0<span class="hljs-selector-class">.102</span>   45<span class="hljs-selector-class">.457</span>   58<span class="hljs-selector-class">.921</span>   29<span class="hljs-selector-class">.557</span>   74<span class="hljs-selector-class">.822</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">218<span class="hljs-selector-class">.5</span>   <span class="hljs-selector-tag">-4</span><span class="hljs-selector-class">.501</span>  23<span class="hljs-selector-class">.001</span>  2<span class="hljs-selector-class">.359</span>  <span class="hljs-selector-tag">-11</span><span class="hljs-selector-class">.9692</span><span class="hljs-selector-class">.967</span>  <span class="hljs-selector-tag">-27</span><span class="hljs-selector-class">.363</span>   18<span class="hljs-selector-class">.361</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">311<span class="hljs-selector-class">.3</span>   21<span class="hljs-selector-class">.963</span> <span class="hljs-selector-tag">-10</span><span class="hljs-selector-class">.663</span> <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.072</span>   15<span class="hljs-selector-class">.685</span>   28<span class="hljs-selector-class">.240</span>   <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.539</span>   44<span class="hljs-selector-class">.464</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">484<span class="hljs-selector-class">.7</span>   65<span class="hljs-selector-class">.114</span>  19<span class="hljs-selector-class">.586</span>  2<span class="hljs-selector-class">.766</span>   49<span class="hljs-selector-class">.300</span>   80<span class="hljs-selector-class">.928</span>   38<span class="hljs-selector-class">.337</span>   91<span class="hljs-selector-class">.891</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">5 7<span class="hljs-selector-class">.36</span><span class="hljs-selector-class">.128</span>   1<span class="hljs-selector-class">.172</span>  0<span class="hljs-selector-class">.122</span>   <span class="hljs-selector-tag">-2</span><span class="hljs-selector-class">.283</span>   14<span class="hljs-selector-class">.540</span>  <span class="hljs-selector-tag">-17</span><span class="hljs-selector-class">.059</span>   29<span class="hljs-selector-class">.316</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">617<span class="hljs-selector-class">.9</span>   22<span class="hljs-selector-class">.408</span>  <span class="hljs-selector-tag">-4</span><span class="hljs-selector-class">.508</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.466</span>   14<span class="hljs-selector-class">.581</span>   30<span class="hljs-selector-class">.235</span>   <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.574</span>   45<span class="hljs-selector-class">.390</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">7 2<span class="hljs-selector-class">.51</span><span class="hljs-selector-class">.278</span>   1<span class="hljs-selector-class">.222</span>  0<span class="hljs-selector-class">.125</span>   <span class="hljs-selector-tag">-6</span><span class="hljs-selector-class">.1138</span><span class="hljs-selector-class">.670</span>  <span class="hljs-selector-tag">-21</span><span class="hljs-selector-class">.559</span>   24<span class="hljs-selector-class">.116</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">827<span class="hljs-selector-class">.3</span>   34<span class="hljs-selector-class">.719</span>  <span class="hljs-selector-tag">-7</span><span class="hljs-selector-class">.419</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.747</span>   28<span class="hljs-selector-class">.400</span>   41<span class="hljs-selector-class">.038</span>   12<span class="hljs-selector-class">.206</span>   57<span class="hljs-selector-class">.232</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">9 5<span class="hljs-selector-class">.9</span>   10<span class="hljs-selector-class">.628</span>  <span class="hljs-selector-tag">-4</span><span class="hljs-selector-class">.728</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.4724</span><span class="hljs-selector-class">.904</span>   16<span class="hljs-selector-class">.351</span>  <span class="hljs-selector-tag">-11</span><span class="hljs-selector-class">.726</span>   32<span class="hljs-selector-class">.981</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">10   23<span class="hljs-selector-class">.9</span>   37<span class="hljs-selector-class">.843</span> <span class="hljs-selector-tag">-13</span><span class="hljs-selector-class">.943</span> <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.390</span>   32<span class="hljs-selector-class">.193</span>   43<span class="hljs-selector-class">.493</span>   15<span class="hljs-selector-class">.509</span>   60<span class="hljs-selector-class">.178</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">11   69<span class="hljs-selector-class">.4</span>   62<span class="hljs-selector-class">.852</span>   6<span class="hljs-selector-class">.548</span>  0<span class="hljs-selector-class">.709</span>   52<span class="hljs-selector-class">.939</span>   72<span class="hljs-selector-class">.766</span>   39<span class="hljs-selector-class">.079</span>   86<span class="hljs-selector-class">.626</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">12   20<span class="hljs-selector-class">.6</span>   18<span class="hljs-selector-class">.296</span>   2<span class="hljs-selector-class">.304</span>  0<span class="hljs-selector-class">.229</span>   13<span class="hljs-selector-class">.036</span>   23<span class="hljs-selector-class">.556</span>   <span class="hljs-selector-tag">-3</span><span class="hljs-selector-class">.943</span>   40<span class="hljs-selector-class">.535</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">131<span class="hljs-selector-class">.9</span>   <span class="hljs-selector-tag">-5</span><span class="hljs-selector-class">.510</span>   7<span class="hljs-selector-class">.410</span>  0<span class="hljs-selector-class">.771</span>  <span class="hljs-selector-tag">-13</span><span class="hljs-selector-class">.6942</span><span class="hljs-selector-class">.674</span>  <span class="hljs-selector-tag">-28</span><span class="hljs-selector-class">.616</span>   17<span class="hljs-selector-class">.596</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">143<span class="hljs-selector-class">.0</span>   14<span class="hljs-selector-class">.956</span> <span class="hljs-selector-tag">-11</span><span class="hljs-selector-class">.956</span> <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.2028</span><span class="hljs-selector-class">.687</span>   21<span class="hljs-selector-class">.224</span>   <span class="hljs-selector-tag">-7</span><span class="hljs-selector-class">.543</span>   37<span class="hljs-selector-class">.455</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">157<span class="hljs-selector-class">.38</span><span class="hljs-selector-class">.860</span>  <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.560</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.169</span>   <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.050</span>   18<span class="hljs-selector-class">.770</span>  <span class="hljs-selector-tag">-14</span><span class="hljs-selector-class">.913</span>   32<span class="hljs-selector-class">.632</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">16   46<span class="hljs-selector-class">.2</span>   29<span class="hljs-selector-class">.831</span>  16<span class="hljs-selector-class">.369</span>  1<span class="hljs-selector-class">.699</span>   21<span class="hljs-selector-class">.745</span>   37<span class="hljs-selector-class">.9176</span><span class="hljs-selector-class">.759</span>   52<span class="hljs-selector-class">.903</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">17   78<span class="hljs-selector-class">.8</span>   78<span class="hljs-selector-class">.016</span>   0<span class="hljs-selector-class">.784</span>  0<span class="hljs-selector-class">.112</span>   62<span class="hljs-selector-class">.105</span>   93<span class="hljs-selector-class">.927</span>   51<span class="hljs-selector-class">.182</span>  104<span class="hljs-selector-class">.850</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="18"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">18   11<span class="hljs-selector-class">.1</span>   13<span class="hljs-selector-class">.167</span>  <span class="hljs-selector-tag">-2</span><span class="hljs-selector-class">.067</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.2096</span><span class="hljs-selector-class">.420</span>   19<span class="hljs-selector-class">.915</span>   <span class="hljs-selector-tag">-9</span><span class="hljs-selector-class">.470</span>   35<span class="hljs-selector-class">.805</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="19"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">198<span class="hljs-selector-class">.6</span>   15<span class="hljs-selector-class">.847</span>  <span class="hljs-selector-tag">-7</span><span class="hljs-selector-class">.247</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.8154</span><span class="hljs-selector-class">.670</span>   27<span class="hljs-selector-class">.024</span>   <span class="hljs-selector-tag">-8</span><span class="hljs-selector-class">.481</span>   40<span class="hljs-selector-class">.175</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="20"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">20   48<span class="hljs-selector-class">.9</span>   50<span class="hljs-selector-class">.727</span>  <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.827</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.184</span>   44<span class="hljs-selector-class">.205</span>   57<span class="hljs-selector-class">.250</span>   28<span class="hljs-selector-class">.156</span>   73<span class="hljs-selector-class">.299</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="21"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">21   22<span class="hljs-selector-class">.1</span>   27<span class="hljs-selector-class">.461</span>  <span class="hljs-selector-tag">-5</span><span class="hljs-selector-class">.361</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.536</span>   21<span class="hljs-selector-class">.671</span>   33<span class="hljs-selector-class">.2515</span><span class="hljs-selector-class">.090</span>   49<span class="hljs-selector-class">.831</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="22"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">22   11<span class="hljs-selector-class">.10</span><span class="hljs-selector-class">.233</span>  10<span class="hljs-selector-class">.867</span>  1<span class="hljs-selector-class">.354</span>  <span class="hljs-selector-tag">-13</span><span class="hljs-selector-class">.486</span>   13<span class="hljs-selector-class">.953</span>  <span class="hljs-selector-tag">-25</span><span class="hljs-selector-class">.362</span>   25<span class="hljs-selector-class">.829</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="23"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">238<span class="hljs-selector-class">.6</span>   22<span class="hljs-selector-class">.627</span> <span class="hljs-selector-tag">-14</span><span class="hljs-selector-class">.027</span> <span class="hljs-selector-tag">-1</span><span class="hljs-selector-class">.395</span>   17<span class="hljs-selector-class">.181</span>   28<span class="hljs-selector-class">.0730</span><span class="hljs-selector-class">.344</span>   44<span class="hljs-selector-class">.911</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="24"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">24   48<span class="hljs-selector-class">.9</span>   48<span class="hljs-selector-class">.961</span>  <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.061</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.006</span>   42<span class="hljs-selector-class">.722</span>   55<span class="hljs-selector-class">.200</span>   26<span class="hljs-selector-class">.470</span>   71<span class="hljs-selector-class">.452</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="25"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">25   22<span class="hljs-selector-class">.1</span>   27<span class="hljs-selector-class">.005</span>  <span class="hljs-selector-tag">-4</span><span class="hljs-selector-class">.905</span> <span class="hljs-selector-tag">-0</span><span class="hljs-selector-class">.490</span>   21<span class="hljs-selector-class">.220</span>   32<span class="hljs-selector-class">.7904</span><span class="hljs-selector-class">.636</span>   49<span class="hljs-selector-class">.374</span></div></div></li></ol></code><code style="margin-left:0px;font-size:12px;font-family:Consolas, 'Liberation Mono', Courier, monospace;border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;" class="hljs python"><ol class="hljs-ln"><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="1"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span style="font-size:16px;"><br><span class="hljs-comment">#求 x1=50, x2=100, x5=10 时的日均营业额的点预测值，置信区间和预测区间（新值预测）</span></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="2"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> x0<-data.frame(x1=<span class="hljs-number">50</span>,x2=<span class="hljs-number">100</span>,x5=<span class="hljs-number">10</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="3"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> predict(fit2, x0)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">   <span class="hljs-number">1</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">17.88685</span> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> predict(fit2,x0, interval=<span class="hljs-string">"confidence"</span>, level=<span class="hljs-number">0.95</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">   fit  lwr  upr</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">1</span> <span class="hljs-number">17.88685</span> <span class="hljs-number">10.98784</span> <span class="hljs-number">24.78585</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> predict(fit2,x0, interval=<span class="hljs-string">"prediction"</span>, level=<span class="hljs-number">0.95</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">   fit   lwr  upr</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-number">1</span> <span class="hljs-number">17.88685</span> <span class="hljs-number">-4.795935</span> <span class="hljs-number">40.56963</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">> </div></div></li></ol></code><div class="hljs-button" data-title="复制"></div></pre><p><span style="font-size:16px;color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;"><br></span></p><span style="color:rgb(255,255,255);font-size:16px;"><strong>6 哑变量回归</strong></span><p style="min-height:1em;letter-spacing:.544px;"><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;">代码化的类别变量成为哑变量或者虚拟变量，在回归模型中使用哑变量时称为哑变量回归或者虚拟变量回归。</span></p><p style="min-height:1em;letter-spacing:.544px;"><span style="color:rgb(26,26,26);font-family:'-apple-system', BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Microsoft YaHei', 'Source Han Sans SC', 'Noto Sans CJK SC', 'WenQuanYi Micro Hei', sans-serif;font-size:16px;"><br></span></p><p style="min-height:1em;letter-spacing:.544px;line-height:27.2px;"><span style="font-size:16px;"><strong>写在</strong></span><strong><span style="font-size:16px;"></span></strong><span style="font-size:16px;"><strong>最后：</strong></span></p><p style="min-height:1em;"><span style="font-size:16px;">至此，多元线性回归预测也完成了，欢迎大家指正，请各位多多转发，给我好看。</span></p><p><br></p><p style="min-height:1em;"><br></p><p style="min-height:1em;letter-spacing:.544px;text-align:center;"><img class="__bg_gif" style="letter-spacing:.544px;" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_gif/Ljib4So7yuWiaWnz8eaGD7hXc0AjkqTaCmjop8Bhlx3zMPutEWkEiaWqHvbq3HhsVNYLbBrqVmsCaIib14adNWAyYw/640?wx_fmt=gif" alt="640?wx_fmt=gif"></p><p style="min-height:1em;letter-spacing:.544px;"><br></p><p><br></p><p style="min-height:1em;font-family:Helvetica, Arial, sans-serif;font-size:16px;line-height:1.5em;"><img src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_jpg/y2fhgP4leThC7KQ2UJCXLjiaPvUncMxWYFjGsuxTficjSSkibncvZiaQdEibarDXIxUOaVzB8xkw9ibqia3xCHT7jYbVg/640?wx_fmt=jpeg" alt="640?wx_fmt=jpeg"></p><p style="min-height:1em;font-family:Helvetica, Arial, sans-serif;line-height:1.5em;"><span 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style="line-height:21px;color:rgb(84,141,212);font-family:'微软雅黑';">人工智能</span><span style="font-family:'微软雅黑';"><span style="line-height:21px;">      三个月入门人工智能</span><br style="line-height:21px;"><span style="line-height:21px;">回复 <span style="color:rgb(84,141,212);">数据分析师</span>   数据分析师成长之路 </span><br style="line-height:21px;"><span style="line-height:21px;">回复</span><span style="line-height:21px;color:rgb(84,141,212);"> 机器学习</span><span style="line-height:21px;">      机器学习的商业应用</span><br style="line-height:21px;"><span style="line-height:21px;">回复 <span style="color:rgb(84,141,212);">数据科学</span>      数据科学实战</span><br style="line-height:21px;"><span style="line-height:21px;">回复 <span style="color:rgb(84,141,212);">常用算法</span>      常用数据挖掘算法</span></span></p></blockquote><img class="__bg_gif" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_gif/y2fhgP4leTgGrcYOTfx4K199arpQnU8MxvSzSnaXeyg1xhpVJkObnU58LzNHicSZZ2q0ib0FtIcBKZzH1D84V8xQ/640?wx_fmt=gif" alt="640?wx_fmt=gif"><img src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_png/y2fhgP4leTgGrcYOTfx4K199arpQnU8MMzl0DPqhS5dvLypvibIWlWbV1Rnu8F0TaIDUpTiaNzmdDicic6Cju1xEicQ/640?wx_fmt=png" alt="640?wx_fmt=png">爱我请给我好看!<img class="__bg_gif" src="https://ss.csdn.net/p?https://mmbiz.qpic.cn/mmbiz_gif/y2fhgP4leTgGrcYOTfx4K199arpQnU8MxvSzSnaXeyg1xhpVJkObnU58LzNHicSZZ2q0ib0FtIcBKZzH1D84V8xQ/640?wx_fmt=gif" alt="640?wx_fmt=gif"></div>
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多元线性回归预测：餐馆营业额与多因素实战

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