Polynomial Linear Regression by Scikit

Suppose we have a 2-degree polynomial function 

And let’s generate some training data sets. First, let’s have some random (x1, x2) sets:

Then, we transform it to (1, x1, x2, x1x2, x1^2, x2^2) form:

For , we know the coefficients is [2, 1, -3, 2, -5, 6]. Then we will have training result:

Let’s make it a little randomly, and we have training result set:

So now our training set is:

Now, we can solve Xtrans, y as how we solve multivariate linear regression:

regr = linear_model.LinearRegression()
regr.fit(X_trans, y)
print regr.coef_    # slope
print regr.intercept_   # intercept

And we got the result, it is very similar to the coefficient we set [2, 1, -3, 2, -5, 6]

Check my code on github.