The Nelson Corporation decides to develop a multiple regression equation to forecast sales performance. A random sample of 14 salespeople is interviewed and given an aptitude test. Also, an index of effort expended is calculated for each salesperson on the basis of a ratio of the mileage on his or her company car to the total mileage projected for adequate coverage of territory. Regression analysis yields the following results:

The quantities in parentheses are the standard errors of the partial regression coefficients. The standard error of the estimate is 3.56. The standard deviation of the sales variable is sy = 16.57. The variables are
Y = the sales performance, in thousands
X1 = the aptitude test score
X2 = the effort index
a. Are the partial regression coefficients significantly different from zero at the .01 significance level?
b. Interpret the partial regression coefficient for the effort index.
c. Forecast the sales performance for a salesperson who has an aptitude test score of 75 and an effort index of .5.
d. Calculate the sum of squared residuals, ˆ‘(Y - )2.
e. Calculate the total sum of squares, ˆ‘(Y - )2.
f. Calculate R2, and interpret this number in terms of this problem.
g. Calculate the adjusted coefficient of determination, 2.

Transcribed Image Text:

Y = 16.57 + .65X, + 20.6X, 05)