%matplotlib inline import random import numpy as np import scipy as sp import pandas as pd import matplotlib.pyplot as plt import seaborn as sns import statsmodels.api as sm import statsmodels.formula.api as smf sns.set_context("talk")
Anscombe's quartet
Anscombe's quartet comprises of four datasets, and is rather famous. Why? You'll find out in this exercise.
anascombe = pd.read_csv('data/anscombe.csv') anascombe.head()
输出结果为:
Part 1
For each of the four datasets...
- Compute the mean and variance of both x and y
- Compute the correlation coefficient between x and y
- Compute the linear regression line: y=β0+β1x+ϵy=β0+β1x+ϵ (hint: use statsmodels and look at the Statsmodels notebook)
print("the mean of x and y are:") print(anascombe.groupby('dataset')['x','y'].mean()) print("the variance of x and y are:") print(anascombe.groupby('dataset')['x', 'y'].var()) print("the correlation coefficient between x and y are:") print(anascombe.groupby('dataset').corr()) print("the first linear regression line:") lin_model_1 = smf.ols('y ~ x', anascombe.groupby('dataset').get_group('I')).fit() print(lin_model_1.params) print("the second linear regression line:") lin_model_2 = smf.ols('y ~ x', anascombe.groupby('dataset').get_group('II')).fit() print(lin_model_2.params) print("the third linear regression line:") lin_model_3 = smf.ols('y ~ x', anascombe.groupby('dataset').get_group('III')).fit() print(lin_model_3.params) print("the fourth linear regression line:") lin_model_4 = smf.ols('y ~ x', anascombe.groupby('dataset').get_group('IV')).fit() print(lin_model_4.params)
输出结果为:
Part 2
Using Seaborn, visualize all four datasets.
hint: use sns.FacetGrid combined with plt.scatter
sns.set(color_codes=True) g = sns.FacetGrid(anascombe, col="dataset") g.map(plt.scatter, "x", "y")
输出结果为: