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I'm trying to build linear, ridge and lasso regression models for at set of data (40 obs., 4 features, 1 response).

I'm building the models using the sklearn package for Python and I can easily find a set of "optimal" coefficients and lambda/alpha values that gives me the lowest possible Mean Squared Error using Grid Search Cross Validation and I find that the lasso regression results in the lowest MSE.

However, I'm skeptical whether or not this is the correct way of doing it compared to using Quadratic Programming to find the optimal values, how would I go about doing this?

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