Data Analysis with Microsoft Excel: Updated for Office 2007

356 Statistical Methods

Notice that walks have a coeffi cient of 0.39, and singles have a coeffi -

cient of 0.47, so a walk has more than 80% of the weight of a single. This

is in contrast to the popular slugging percentage used to measure the offen-

sive production of players, which gives weight 0 to walks, 1 to singles, 2 to

doubles, 3 to triples, and 4 to home runs. The Rosner-Woods equation gives

relatively more weight to singles, and the weight for doubles is less than

twice as much as the weight for singles. Similar comparisons are true for

triples and home runs. Do baseball general managers use equations like the

Rosner-Woods equation to evaluate ball players? If not, why not?

You can also use regression to see whether a particular group is being

discriminated against. A company might ask whether women are paid less

than men with comparable jobs. You can include a term in a regression to

account for the effect of gender. Alternatively, you can fi t a regression model

for just men, apply the model to women, and see whether women have sala-

ries that are less than would be predicted for men with comparable posi-

tions. It is now common for such arguments to be offered as evidence in

court, and many statisticians have experience in legal proceedings.

Regression Example: Predicting Grades

For a detailed example of a multiple regression, consider the Calculus

workbook fi rst discussed in Chapter 8, which examined how scores in fi rst-

semester calculus were related to various measures of student achievement

in high school (Edge and Friedberg, 1984).

To open the Calculus workbook:

1 Start Excel and open the Calculus workbook from the Chapter09

data folder.

2 Save the fi le as Calculus Multiple Regression.

In Chapter 8, it appeared from the correlation matrix and scatter plot ma-

trix that the algebra placement test is the best individual predictor of the

fi rst semester calculus score (although it is not very successful). Multiple re-

gression gives a measure of how good the predictors are when used together.

The model is

Calculus score5b 0 1b 11 Calc HS 2 1b 21 ACT Math 2 1b 31 Alg Place 2

1b 41 Alg2 Grade^2 1b 51 HS Rank^2 1b 61 Gender Code^2 1e