如何在statsmodels OLS中计算截距和斜率?

问题描述

在这里我问如何在线性模型中计算AIC.如果我将 LinearRegression()方法替换为 linear_model.OLS 方法以获得AIC，那么如何为OLS线性模型计算斜率和截距?

Here I asked how to compute AIC in a linear model. If I replace LinearRegression() method with linear_model.OLS method to have AIC, then how can I compute slope and intercept for the OLS linear model?

import statsmodels.formula.api as smf
regr = smf.OLS(y, X, hasconst=True).fit()

推荐答案

在您的示例中，您可以使用 regr 的 params 属性，该属性将显示系数和截距.它们的关键是您首先需要向X数据添加 1.0 s的列向量.为什么?从技术上讲，截距项只是对列向量1s的系数.也就是说，截距只是一个系数，当乘以X的项" 1.0时，会产生自身.将其添加到其他系数和特征的总和后，即可得到nx1个预测值数组.

In your example, you can use the params attribute of regr, which will display the coefficients and intercept. They key is that you first need to add a column vector of 1.0s to your X data. Why? The intercept term is technically just the coefficient to a column vector of 1s. That is, the intercept is just a coefficient which, when multiplied by an X "term" of 1.0, produces itself. When you add this to the summed product of the other coefficients and features, to get your nx1 array of predicted values.

下面是一个例子.

# Pull some data to use in the regression
from pandas_datareader.data import DataReader
import statsmodels.api as sm

syms = {'TWEXBMTH' : 'usd',
        'T10Y2YM' : 'term_spread',
        'PCOPPUSDM' : 'copper'
       }

data = (DataReader(syms.keys(), 'fred', start='2000-01-01')
        .pct_change()
        .dropna())
data = data.rename(columns = syms)
# Here's where we assign a column of 1.0s to the X data
# This is required by statsmodels
# You can check that the resulting coefficients are correct by exporting
# to Excel with data.to_clipboard() and running Data Analysis > Regression there
data = data.assign(intercept = 1.)

现在实际运行回归并获取系数仅需要1行.

Now actually running the regression and getting coefficients takes just 1 line in addition to what you have now.

y = data.usd
X = data.loc[:, 'term_spread':]
regr = sm.OLS(y, X, hasconst=True).fit()
print(regr.params)
term_spread   -0.00065
copper        -0.09483
intercept      0.00105
dtype: float64

因此，关于您在 AIC ，您需要确保在调用 .fit 之前，X数据在其中也具有常量.

So regarding your question on AIC, you'll want to make sure the X data has a constant there as well, before you call .fit.

注意:调用 .fit 时，您将创建一个回归结果包装器，并且可以访问此处.

Note: when you call .fit, you create a regression results wrapper and can access any of the attributes lists here.

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