Is it useful or even necessary to standardize independent variables for linear regression?

Question

When performing a linear multiple regression $ Y = X_1 + X_2 $ is it necessary that $ X_1 $ and $ X_2 $ provide the same scale?
When I think of the variables being represented by an orthogonal axis, it shouldn't matter, or ?

Source

Stephan Kolassa · Answer

It is sometimes useful, but never (IMO) necessary. A linear rescaling of your predictors amounts precisely to changing the labels on their axes, in a linear way.
If, for instance, you rescale a predictor such that it has a standard deviation of 1, then you can interpret the corresponding regression coefficient estimate as the change in the dependent variable associated with a 1 SD change in the predictor. This may or may not be more enlightening than leaving your predictors as they are and then interpreting the estimates as the change in the DV associated to a change of 1lb or 1 horsepower.

Is it useful or even necessary to standardize independent variables for linear regression?

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