How are standardized regression coefficients used in real statistics?
If the # of columns in Rx = the # of rows in Rc (i.e. Rc does not contain an intercept coefficient) then standardized regression coefficients are based on the y data also being standardized; while if Rc contains one more row than the # of columns in Rx the standardized regression coefficients are based on the y data in Ry not being standardized.
How to calculate the standard error of regression?
We can now calculate the standardized regression coefficients and their standard errors, as shown in range E9:G11, using the above formulas. E.g. the standard regression coefficient for Color (cell F10) can be calculated by the formula =F5*A17/C17. The standard error for this coefficient (cell G10) can be calculated by =G5*A17/C17.
What is the regression coefficient of the j th predictor?
The regression coefficient of the j -th predictor is β ^ j S j. In the presented case, I have assumed that only the predictors had been standardized. If one also standardizes the response variable, transforming the covariate coefficients back to the original scale is done by using the formula from the reference you gave.
Can a regression be converted to a standardized form?
So the assumed form for the regression line is incorrect for the standardized case. Nevertheless, the derivation is correct. If you set the intercept vector in the final result to zero, you will convert the coefficients back to non-standardized form. Thanks for contributing an answer to Cross Validated!
How to assess the relative contribution of a predictor?
For each predictor of which you want to assess the relative contribution, you need to specify two models. The first model contains all predictors that already figure in your regression model, and the second model is the same with the exception that it omits the predictor of interest.
How to evaluate the contribution of a linear regression model?
Say I build a linear regression model to identify linear dependencies between variables in my data. Some of these variables are categorical variables. If I want to evaluate the contribution of a given predictor, how do I evaluate it?