数据分析习题Python
本次作业是emu193教程的课后作业，来源自：
https://nbviewer.jupyter.org/github/schmit/cme193-ipython-notebooks-lecture/blob/master/Exercises.ipynbPart 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: (hint: use statsmodels and look at the Statsmodels notebook)
第一部分主要是要求我们对读入的数据进行分析，求出均值，方差，相关系数，线性拟合等等。代码如下
# coding: utf-8
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")
anascombe = pd.read_csv('anscombe.csv')
anascombe.head()
print("\nThe mean of x and y:")
print(anascombe.groupby(['dataset']).mean())
print("\nThe varience of x and y:")
print(anascombe.groupby(['dataset']).var())
print("\nThe correlation coefficient of x and y:")
print(anascombe.groupby(["dataset"]).corr())
keys = ['I', 'II', 'III', 'IV']
for k in keys:
lin_model = smf.ols('y ~ x', anascombe[anascombe['dataset'] == k]).fit()
print('\nThe linear model for dataset', k)
print(lin_model.summary())运行结果如下：
The mean of x and y:
x y
dataset
I 9.0 7.500909
II 9.0 7.500909
III 9.0 7.500000
IV 9.0 7.500909
The varience of x and y:
x y
dataset
I 11.0 4.127269
II 11.0 4.127629
III 11.0 4.122620
IV 11.0 4.123249
The correlation coefficient of x and y:
x y
dataset
I x 1.000000 0.816421
y 0.816421 1.000000
II x 1.000000 0.816237
y 0.816237 1.000000
III x 1.000000 0.816287
y 0.816287 1.000000
IV x 1.000000 0.816521
y 0.816521 1.000000
The linear model for dataset I
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.667
Model: OLS Adj. R-squared: 0.629
Method: Least Squares F-statistic: 17.99
Date: Mon, 11 Jun 2018 Prob (F-statistic): 0.00217
Time: 18:10:13 Log-Likelihood: -16.841
No. Observations: 11 AIC: 37.68
Df Residuals: 9 BIC: 38.48
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 3.0001 1.125 2.667 0.026 0.456 5.544
x 0.5001 0.118 4.241 0.002 0.233 0.767
==============================================================================
Omnibus: 0.082 Durbin-Watson: 3.212
Prob(Omnibus): 0.960 Jarque-Bera (JB): 0.289
Skew: -0.122 Prob(JB): 0.865
Kurtosis: 2.244 Cond. No. 29.1
==============================================================================
The linear model for dataset II
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.666
Model: OLS Adj. R-squared: 0.629
Method: Least Squares F-statistic: 17.97
Date: Mon, 11 Jun 2018 Prob (F-statistic): 0.00218
Time: 18:10:13 Log-Likelihood: -16.846
No. Observations: 11 AIC: 37.69
Df Residuals: 9 BIC: 38.49
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 3.0009 1.125 2.667 0.026 0.455 5.547
x 0.5000 0.118 4.239 0.002 0.233 0.767
==============================================================================
Omnibus: 1.594 Durbin-Watson: 2.188
Prob(Omnibus): 0.451 Jarque-Bera (JB): 1.108
Skew: -0.567 Prob(JB): 0.575
Kurtosis: 1.936 Cond. No. 29.1
==============================================================================
The linear model for dataset III
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.666
Model: OLS Adj. R-squared: 0.629
Method: Least Squares F-statistic: 17.97
Date: Mon, 11 Jun 2018 Prob (F-statistic): 0.00218
Time: 18:10:13 Log-Likelihood: -16.838
No. Observations: 11 AIC: 37.68
Df Residuals: 9 BIC: 38.47
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 3.0025 1.124 2.670 0.026 0.459 5.546
x 0.4997 0.118 4.239 0.002 0.233 0.766
==============================================================================
Omnibus: 19.540 Durbin-Watson: 2.144
Prob(Omnibus): 0.000 Jarque-Bera (JB): 13.478
Skew: 2.041 Prob(JB): 0.00118
Kurtosis: 6.571 Cond. No. 29.1
==============================================================================
The linear model for dataset IV
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.667
Model: OLS Adj. R-squared: 0.630
Method: Least Squares F-statistic: 18.00
Date: Mon, 11 Jun 2018 Prob (F-statistic): 0.00216
Time: 18:10:13 Log-Likelihood: -16.833
No. Observations: 11 AIC: 37.67
Df Residuals: 9 BIC: 38.46
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 3.0017 1.124 2.671 0.026 0.459 5.544
x 0.4999 0.118 4.243 0.002 0.233 0.766
==============================================================================
Omnibus: 0.555 Durbin-Watson: 1.662
Prob(Omnibus): 0.758 Jarque-Bera (JB): 0.524
Skew: 0.010 Prob(JB): 0.769
Kurtosis: 1.931 Cond. No. 29.1
==============================================================================Part 2
Using Seaborn, visualize all four datasets.
hint: use sns.FacetGrid combined with plt.scatter
这部分主要是对数据进行可视化处理，Python代码如下
# coding: utf-8
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")
anascombe = pd.read_csv('anscombe.csv')
anascombe.head()
m = sns.FacetGrid(anascombe, col="dataset")
m.map(plt.scatter, "x","y") 运行结果如下：
