I have basic understanding of how to perform linear regression with sklearn and statsmodels. There are several questions that I would like to ask regarding Linear Regression (OLS estimator) :
Is standardization always necessary for OLS estimator? I am still learning a bit of theoretical aspect of regression analysis. Standardization is mentioned in my data science class but almost None throughout my study in regression analysis. If no, when do I apply standardization (also do I need to standardize the predicted variable)?
I tried comparing both, in terms of evaluation metrics(mse) the results are relatively similar, but in terms of coefficient it is very different (due to different scales of predictors). If this is the case how to compare the significance of a predictor?
I tried comparing the result with statsmodel OLS on unstandardized data. Coefficient result is different by huge margin and on top of that mean squared error is worse with statsmodel than with sklearn model. However, sklearn model is less informative in terms of statistical information, for example if I want to remove a variable based on p-value from regression result. Is this supposed to happen(different result)?