1、先安裝好jupyter，然後打開。、
2、完成以下問題：
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+ϵy=β0+β1x+ϵ (hint: use statsmodels and look at the Statsmodels notebook)
導入所需模塊和所要處理的數據：
Compute the mean and variance of both x and y：
In [26]:
# 先把四個分組分離出來
anascombe_group = anascombe.groupby('dataset')
dataset_names = ['I', 'II', 'III', 'IV']
# x和y在四個分組中的均值和方差
for i in dataset_names:
print('dataset', i, ': ')
print(' x均值: ', anascombe_group.get_group(i)['x'].mean())
print(' x方差: ', anascombe_group.get_group(i)['x'].var())
print(' y均值: ', anascombe_group.get_group(i)['y'].mean())
print(' y方差: ', anascombe_group.get_group(i)['y'].var())dataset I :
x均值: 9.0
x方差: 11.0
y均值: 7.500909090909093
y方差: 4.127269090909091
dataset II :
x均值: 9.0
x方差: 11.0
y均值: 7.500909090909091
y方差: 4.127629090909091
dataset III :
x均值: 9.0
x方差: 11.0
y均值: 7.500000000000001
y方差: 4.12262
dataset IV :
x均值: 9.0
x方差: 11.0
y均值: 7.50090909090909
y方差: 4.12324909090909Compute the correlation coefficient between x and y:
In [27]:
# x和y的相關係數
print('相關係數：')
print(anascombe.groupby('dataset').corr())Out [27]:
相關係數：
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 1.000000Compute the linear regression line: y=β0+β1x+ϵy=β0+β1x+ϵ (hint: use statsmodels and look at the Statsmodels notebook)
In [28]:
# 線性迴歸方程
for i in dataset_names:
x = anascombe_group.get_group(i)['x']
y = anascombe_group.get_group(i)['y']
X = sm.add_constant(x)
model = sm.OLS(y,X)
results = model.fit()
print(results.summary())
print('\nparams:', results.params, '\n\n')Out [28]:
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: 13:25:48 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]
------------------------------------------------------------------------------
const 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.
params: const 3.000091
x 0.500091
dtype: float64
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: 13:25:48 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]
------------------------------------------------------------------------------
const 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.
params: const 3.000909
x 0.500000
dtype: float64
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: 13:25:48 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]
------------------------------------------------------------------------------
const 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.
params: const 3.002455
x 0.499727
dtype: float64
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: 13:25:48 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]
------------------------------------------------------------------------------
const 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.
params: const 3.001727
x 0.499909
dtype: float64
Part 2
Using Seaborn, visualize all four datasets.
hint: use sns.FacetGrid combined with plt.scatter
In [30]:
fig = sns.FacetGrid(anascombe, col='dataset')
fig.map(plt.scatter, 'x', 'y')
plt.show()Out [30]:
參考資料：