第十四周作业

Anscombe's quartet

Anscombe's quartet comprises of four datasets, and is rather famous. Why? You'll find out in this exercise.

模块：

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")

数据：

anascombe = sns.load_dataset("anscombe")
print(anascombe)

         

           

Part1

计算均值、方差：

print("\nMean:")
print(anascombe.groupby("dataset").mean())
print("\nVariance:")
print(anascombe.groupby("dataset").var())

结果：

             

计算相关系数：

print("\nCorrelation coefficient:")
print(anascombe.groupby("dataset").x.corr(anascombe.y))

    或

X = []
Y = []
coefficients = []
for i in range(0, 4):
    X.append(anascombe.x[i*11:i*11+11].values)
    Y.append(anascombe.y[i*11:i*11+11].values)
    coefficients.append(sp.stats.pearsonr(X[i], Y[i])[0])
    print(coefficients[i])

结果：

          

  

计算线性回归方程：

for i in range(0,4):
    x = X[i]
    x = sm.add_constant(x)
    model = sm.OLS(Y[i], x)
    results = model.fit()
    print("\nThe linear regression " + str(i+1))
    print(" y = "+str(results.params[0])+"+"+str(results.params[1])+"x")

结果：

Part2

散点图及回归直线：

sns.lmplot(x="x", y="y", col="dataset", hue="dataset", data=anascombe,
           col_wrap=2, ci=None, palette="muted", size=4,
           scatter_kws={"s": 80, "alpha": 1})
plt.show()