有没有办法从使用 sklearn 进行多元线性回归的预测中获取解释变量的值？

Question

I'm trying to understand if there is a way, using the sklearn.linear_model.LinearRegression() to get the values for the explanatory variables, given a prediction of X .

For example - looking at MPG of a car. I can build the model using multiple explanatory variables and then predict (successfully) the MPG for a given set of X. However, can I do the reverse and give Y and then get the predict X values?

Sorry if not very clear!

Answer 1

When approximating some values Y associated to some points X using linear regression what we are looking is for the nearest linear function (f(x) = ax + k) to the points in a least square sense. So you are not getting Y but you are rather getting the linear function that best approximates your input.

Can you do the opposite that is build a function that predicts $X$ rather than $Y$. Consider the example in sklearn.linear_model.LinearRegression we are going to tune it a bit.

>>> import numpy as np
>>> from sklearn.linear_model import LinearRegression
>>> X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
>>> # y = 1 * x_0 + 2 * x_1 + 3
>>> y = np.dot(X, np.array([1, 2])) + 3
>>> # Changing y <-> X 
>>> reg = LinearRegression().fit(y, X)
>>> # Changing y <-> X 
>>> reg.score(y, X)
0.8269230769230769
>>> reg.coef_
array([[0.23076923],
       [0.38461538]])
>>> reg.intercept_
array([-0.46153846, -1.26923077])
>>> reg.predict(np.array([[16.]]))
array([[3.23076923, 4.88461538]])

This could let you predict your explanatory variables from the MPG of your vehicles. Although this works take into account that this approach will probably give you very bad results as you are trying to approach a cloud of points inside a multidimensional space with a line inside that space. Take a look at your score before trying to predict anything with your model.