LinearModel.fit - are the regression coefficient standardized?

Hello at all, I have a multiple linear regression done with LinearModel.fit and got estimate values (b) for the independent data X. I want to compare the regressions coefficients (estimated values) with each other to estimate the influence on the responce in y.

Here my questions: Are the estimated values comparable to each other or how can I do this? I don't have an vector of all b for different X. Only one value for one X(i). So I can't standardize them with zscore. Is there a command to get the standardized values or an other trick? Of course I could standardize all data at the beginning, but the results are realy confusing, so I hope anybody has a better solution for me.

Thank you very much. Greets

Answer 1

[Tom Lane]

I don't quite understand what you want. The coefficient estimates as shown are not standardized. The so-called "beta coefficients" are the coefficients for standardized X values, and indeed the easiest way to get them would be to standardize X beforehand, such as by using zscore(X).

Here's another idea. If you try the following, you may conclude that the two coefficients are not comparable because one multiples a predictor with values in the 1000s, and the other multiplies a predictor with values close to 1:

load carsmall
lm = LinearModel.fit([Weight Cylinders],MPG)

There is a plot intended to show the effects of these predictors on a common scale:

plotEffects(lm)

This plot shows the estimated effect on the response of changing each predictor from its minimum value to its maximum value.

[Greg Heath]

I would standardize both X and y.