Beta coefficients in multiple regression

#1
Hi guys.

I have a question about beta coefficients that are calculated
for standard multiple linear regression procedure. I kind of don't understand
about how they indeed are calculated. They are regression coefficients
that occur when predictors are standardized to have zero mean and 1
standard error. I thought they are just raw coefficients multiplied by
corresponding raw predictor's standard errors. But it seems like it's not true.

Any thoughts on how they are calculated ?

Thanks in advance.
 

Masteras

TS Contributor
#2
It is exactly what you said. you standardize the predictors first (from each variable or column you subtract its mean and divide by the standard deviation) and then you perform the classical multiple linear regression. But their interpretation is also a bit different.
 

Dragan

Super Moderator
#3
Any thoughts on how they are calculated ?

Thanks in advance.

You can compute the j-th standardized regression weight as:

beta_j = b_j * (S_j / S_Y) where

b_j is the usual OLS unstandardized regression weight and S_j and S_Y are the standard deviations associated with the j-th independent variable and the dependent variable (Y), respectively.


Note: If you want to compute them through a regression analysis you have to standardize all variables including the dependent variable (Y) before perfoming the regression.
 
#4
You can compute the j-th standardized regression weight as:

beta_j = b_j * (S_j / S_Y) where

b_j is the usual OLS unstandardized regression weight and S_j and S_Y are the standard deviations associated with the j-th independent variable and the dependent variable (Y), respectively.


Note: If you want to compute them through a regression analysis you have to standardize all variables including the dependent variable (Y) before perfoming the regression.

Thank you. I'm using StatSoft Statistica. It computes both B and Beta coefficients. So beta coefficients look like correlations, right ? At least it's true for one-variable regression analysis.
 

JenB

New Member
#5
I know this is an old thread, but I thought I'd mention that STATISTICA has different representations of regression coefficients.

Prior to Version 9:
  • Beta: standardized
  • B: non-standardized

Version 9 and beyond:
  • b*: standardized
  • b: non-standardized

The standardized beta (b*) are the coefficients you would have obtained had you first standardized all of your variables to a mean of 0 and a standard deviation of 1. Thus, the magnitude of these b* coefficients allow you to compare the relative contribution of each independent variable in the prediction of the dependent variable.

The non-standardized beta (b) is used more generally.

From the Multiple Regression Results dialog, you can access values for both the standardized beta (b*) and the non-standardized beta (b) by clicking the "Regression results" button.

Hope this helps...
 
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