高级编程技术（Python）作业16
题目来源：
https://nbviewer.jupyter.org/github/schmit/cme193-ipython-notebooks-lecture/blob/master/Exercises.ipynb
Solution：
print("the mean of x and y:")
print(anascombe.groupby(["dataset"])[['x', 'y']].mean())
print("the variance of x and y:")
print(anascombe.groupby(["dataset"])[['x', 'y']].var())
print("the correlation coefficient between x and y:")
print(anascombe.groupby(["dataset"])[['x', 'y']].corr())
datasets = ['I', 'II', 'III', 'IV']
for dataset in datasets:
lin_model = smf.ols('y ~ x', anascombe[anascombe["dataset"] == dataset]).fit()
print('\nThe linear model for dataset %s:' %(dataset))
print(lin_model.summary())Output：
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 variance 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 between 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: Tue, 12 Jun 2018 Prob (F-statistic): 0.00217
Time: 21:58:05 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
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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: Tue, 12 Jun 2018 Prob (F-statistic): 0.00218
Time: 21:58:05 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
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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: Tue, 12 Jun 2018 Prob (F-statistic): 0.00218
Time: 21:58:05 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
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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: Tue, 12 Jun 2018 Prob (F-statistic): 0.00216
Time: 21:58:05 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
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
c:\python\python36-32\lib\site-packages\scipy\stats\stats.py:1394: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=11
"anyway, n=%i" % int(n))
c:\python\python36-32\lib\site-packages\scipy\stats\stats.py:1394: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=11
"anyway, n=%i" % int(n))
c:\python\python36-32\lib\site-packages\scipy\stats\stats.py:1394: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=11
"anyway, n=%i" % int(n))
c:\python\python36-32\lib\site-packages\scipy\stats\stats.py:1394: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=11
"anyway, n=%i" % int(n))注释：这里代码最后报了UserWarning错误，我查看了一下是在生成线性模型的时候，函数本身计算了一个kurtosistest的函数，而这个函数的参数要求是大于20的，所以会报一个无关紧要的UserWarning，如果想要忽略这个错误，可以使用
import warnings
warnings.filterwarnings("ignore")来消除这个warning。
Solution：
g = sns.FacetGrid(anascombe, col='dataset')
g.map(plt.scatter, 'x', 'y') Output：
