Python学习之路_jupyter notebook

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()

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	dataset	x	y
0	I	10.0	8.04
1	I	8.0	6.95
2	I	13.0	7.58
3	I	9.0	8.81
4	I	11.0	8.33

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: $y = \beta_0 + \beta_1 x + \epsilon$ (hint: use statsmodels and look at the Statsmodels notebook)

def get_data(data):
    return pd.Series([data['x'].mean(), data['x'].var(), data['y'].mean(), data['y'].var()],index=['x均值', 'x方差', 'y均值', 'y方差'])

dataset_name = anascombe.dataset.unique()
group = anascombe.groupby(by=list(["dataset"]))
for name in dataset_name:
    data = group.get_group(name)
    print('dataset: ', name)
    print(pd.DataFrame(get_data(data)))
    print('系数')
    print(data.corr(),'\n')
    x = data['x']
    X = sm.add_constant(data['x'])
    y = data['y']
    model = sm.OLS(y,X)
    results = model.fit()
    print(results.params)
    y_fitted = results.fittedvalues
    fig, ax = plt.subplots()
    ax.plot(x, y, 'o', label='data')
    ax.plot(x, y_fitted, 'r-',label='OLS')
    ax.legend(loc='best')
    plt.show()
    print('\n')

dataset:  I
             0
x均值   9.000000
x方差  11.000000
y均值   7.500909
y方差   4.127269
系数
          x         y
x  1.000000  0.816421
y  0.816421  1.000000 

const    3.000091
x        0.500091
dtype: float64

dataset:  II
             0
x均值   9.000000
x方差  11.000000
y均值   7.500909
y方差   4.127629
系数
          x         y
x  1.000000  0.816237
y  0.816237  1.000000 

const    3.000909
x        0.500000
dtype: float64

dataset:  III
            0
x均值   9.00000
x方差  11.00000
y均值   7.50000
y方差   4.12262
系数
          x         y
x  1.000000  0.816287
y  0.816287  1.000000 

const    3.002455
x        0.499727
dtype: float64

dataset:  IV
             0
x均值   9.000000
x方差  11.000000
y均值   7.500909
y方差   4.123249
系数
          x         y
x  1.000000  0.816521
y  0.816521  1.000000 

const    3.001727
x        0.499909
dtype: float64

Part 2

Using Seaborn, visualize all four datasets.

hint: use sns.FacetGrid combined with plt.scatter

    g = sns.FacetGrid(anascombe, col="dataset", size=4)
    g = g.map(plt.scatter, "x", "y", edgecolor="w")