Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 9 Multiple Regression 355

To change the p value:

1 Click the Critical Value box, type 0.10, and then press Enter. This

gives you the critical value for the F test at the 10% signifi cance

level.

Notice that the critical value shifts to the left, telling you that 10% of the

values of the F distribution lie to the right of this point.

Continue working with the F distribution worksheet, trying different

parameter values to get a feel for the F distribution. Close the workbook

when you’re fi nished. You do not need to save any changes you may have

inadvertently made to the document.

Using Regression for Prediction

One of the goals of regression is prediction. For example, you could use

regression to predict what grade a student would get in a college calculus

course. (This is the dependent variable, the one being predicted.) The pre-

dictors (the independent variables) might be ACT or SAT math score, high

school rank, and a placement test score from the fi rst week of class. Students

with low predictions might be asked to take a lower-level class.

However, suppose the dependent variable is the price of a four-unit apart-

ment building and the independent variables are the square footage, the age of

the building, the total current rent, and a measure of the condition of the build-

ing. Here you might use the predictions to fi nd a building that is undervalued,

with a price that is much less than its prediction. This analysis was actually

carried out by some students, who found that there was a bargain building

available. The owner needed to sell quickly as a result of cash fl ow problems.

You can use multiple regression to see how several variables combine

to predict the dependent variable. How much of the variability in the de-

pendent variable is accounted for by the predictors? Do the combined in-

dependent variables do better or worse than you might expect, on the basis

of their individual correlations with the dependent variable? You might be

interested in the individual coeffi cients and in whether they seem to mat-

ter in the prediction equation. Could you eliminate some of the predictors

without losing much prediction ability?

When you use regression in this way, the individual coeffi cients are impor-

tant. Rosner and Woods (1988) compiled statistics from baseball box scores, and

they regressed runs on singles, doubles, triples, home runs, and walks (walks

are combined with hit by pitched ball). Their estimated prediction equation is

Runs 52 2.49 1 0.47 singles 1 0.76 doubles 1 1.14 triples 1 1.54 home runs 1 0.39 walks