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# Comparing Coefficients of Different Scales

Definition
Let me define the influence of an independent variable on the dependent variable as the change in the dependent variable due to the independent variable.

Background
Suppose that your company has a nationwide hiring program, and you have determined with data consisting of SALES (\$M) in the first year on the job, undergraduate GPA, years of experience since graduation (EXP), the quality of their undergraduate institution (RANK), and performance on the Wonderlic test (TEST) that

SALES = 1.23 + 5.03*GPA + .14*EXP - .41*RANK + .38*TEST

The various coefficients cannot be compared directly because each of the independent variables is measured on a different scale. GPA is measured on a scale from 0.0 to 4.0, EXP ranges from 0 to 3, RANK ranges from 1 to 4 (with 1 being the highest best), and TEST ranges from 0 to 50.

Problem
You want to know what attributes of those graduates have the biggest influence on SALES. No credit will be given for an opinion. Compute the influence of each independent variable. Which two variables should you place the most importance on, and base the decision to hire on?

Hint
Since neither the raw data nor the regression analysis is given, you will not be able to quantify influence using standardized regression coefficients (valid, but not described in text) or coefficients of partial determination (valid and described in text). All the information needed to compute influence is contained in the Background statement.

#### Solution Preview

One way I see to solve this problem is to re-normalize the variables to a standard, say from 0 to 1. Write

SALES = 1.23 + 5.03*GPA + .14*EXP - .41*RANK + .38*TEST

in the following equivalent way:

SALES = 1.23 + 5.03*4*(GPA/4) + .14*3*(EXP/3) - ...

#### Solution Summary

We re-normalize the independent variables to see, in an easier manner, the influence of each of them in the dependent variable.

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