14周 Anscombe's quartet

最新推荐文章于 2025-02-06 15:27:21 发布

原创最新推荐文章于 2025-02-06 15:27:21 发布 · 256 阅读

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本文通过Python的statsmodels库计算了Anscombe四组数据集的x与y的均值、方差及相关系数，并利用Seaborn进行了可视化展示。同时使用线性回归分析了各数据集间的联系。

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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+ϵ (hint: use statsmodels and look at the Statsmodels notebook)

Part 2

Using Seaborn, visualize all four datasets.

hint: use sns.FacetGrid combined with plt.scatte

import pandas as pd
import seaborn as se

import matplotlib.pyplot as plt
import statsmodels.api as st



ans = se.load_dataset('anscombe')  
df = ans.groupby('dataset')
mean_var = pd.concat([df.mean(), df.var()], keys=['mean', 'variance'])
corr = pd.concat([df.corr()], keys=['correlation'])
print(mean_var)
print(corr)

data_dict = dict(list(df))
array_x, array_y = {}, {}
for key, value in data_dict.items():
    array_x[key] = value['x'].values
    array_y[key] = value['y'].values
for key in array_x.keys():
    x = st.add_constant(array_x[key])
    y = array_y[key]
    est = st.OLS(y, x).fit()
    params = est.params
    print(key, ': beta0 =', params[0], 'beta1 =', params[1])

se.set(style='whitegrid')
g = se.FacetGrid(ans, col="dataset", hue="dataset")
g.map(plt.scatter, 'x', 'y')
plt.show()