3.1.3.2 多元回归: 包含多因素

考虑用2个变量x和y来解释变量z的线性模型:

$z = x \, c_1 + y \, c_2 + i + e$

这个模型可以被视为在3D世界中用一个平面去拟合 (x, y, z) 的点云。

3.1.3.2 多元回归: 包含多因素 - 图1

实例: 鸢尾花数据 (examples/iris.csv)

萼片和花瓣的大小似乎是相关的: 越大的花越大! 但是，在不同的种之间是否有额外的系统效应?

3.1.3.2 多元回归: 包含多因素 - 图2

In [33]:

  1. data = pandas.read_csv('examples/iris.csv')
  2. model = ols('sepal_width ~ name + petal_length', data).fit()
  3. print(model.summary())
  1.                             OLS Regression Results                            
  2.  ==============================================================================
  3. Dep. Variable:            sepal_width   R-squared:                       0.478
  4. Model:                            OLS   Adj. R-squared:                  0.468
  5. Method:                 Least Squares   F-statistic:                     44.63
  6. Date:                Thu, 19 Nov 2015   Prob (F-statistic):           1.58e-20
  7. Time:                        09:56:04   Log-Likelihood:                -38.185
  8. No. Observations:                 150   AIC:                             84.37
  9. Df Residuals:                     146   BIC:                             96.41
  10. Df Model:                           3                                         
  11. Covariance Type:            nonrobust                                         
  12.  ======================================================================================
  13.                          coef    std err          t      P>|t|      [95.0% Conf. Int.]
  14.  ------------- ------------- ------------- ------------- ------------- ---------------------
  15. Intercept              2.9813      0.099     29.989      0.000         2.785     3.178
  16. name[T.versicolor]    -1.4821      0.181     -8.190      0.000        -1.840    -1.124
  17. name[T.virginica]     -1.6635      0.256     -6.502      0.000        -2.169    -1.158
  18. petal_length           0.2983      0.061      4.920      0.000         0.178     0.418
  19.  ==============================================================================
  20. Omnibus:                        2.868   Durbin-Watson:                   1.753
  21. Prob(Omnibus):                  0.238   Jarque-Bera (JB):                2.885
  22. Skew:                          -0.082   Prob(JB):                        0.236
  23. Kurtosis:                       3.659   Cond. No.                         54.0
  24.  ==============================================================================
  26. Warnings:
  27. [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.