第十四周作业

最新推荐文章于 2025-03-14 22:09:59 发布

AD_Jadson

最新推荐文章于 2025-03-14 22:09:59 发布

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本文链接：https://blog.youkuaiyun.com/AD_Jadson/article/details/80657426

本博客通过计算均值、方差、相关系数等统计指标，对比了Anscombe四重奏数据集的相似之处，并利用散点图和线性回归展示了数据集间的显著差异。尽管这些数据集在统计特性上几乎一致，但其实际分布却大相径庭。

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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()