Regression question

#1
I am just beginning to learn about regression and I have a couple of questions.

What is the difference in the standardized regression coefficient and the unstandardized regression coefficient?

Also, what is the difference in the interpretation of the prediction equation when using the standardized regression coefficient and using the unstandardized regression coefficient?

Thank you very much for any help!!!:)
 
#2
Here's how to get the standardized regression coefficients: before fitting the regression equation, all variables--response and predictors--are standardized by subtracting the mean and dividing by the standard deviation. The standardized regression coefficients, then, represent the change in response for a change of one standard deviation in a predictor.
 

JohnM

TS Contributor
#3
Diane,

The difference is that the standardized regression coefficient is based on converting all of the data points into z scores (or standard scores):

z = (x - mu) / s

which represent the number of standard deviations an individual score is from its mean (as in the normal distribution).

The interpretation of the equation is basically the same, whether it is standardized or unstandardized, however, the with the standardized regression, you can more easily determine the percent contribution of each coefficient (independent variable) in the equation.

Sometimes, when you have several independent variables in a regression model, and they all have widely different measurement scales, it can make the picture a bit more clear by converting everything to standard scores.

Here's a good link: http://www.csulb.edu/~msaintg/ppa696/696regmx.htm#STANDARDIZED

Hope this helps a bit,
John