572 Chapter 15 Multiple Regression
c. What would we predict in a different city that was identical in every way except that it
spent $100 per capita on social services?
15.2 Refer to Exercise 15.1. Assume that
b5 [ 2 0.438 0.762 .081 2 0.132]
Interpret the results.
15.3 For the values of in Exercise 15.2, the corresponding standard errors are
[0.397 0.252 .052 .025]
Which, if any, predictor would you be most likely to drop if you wanted to refine your re-
gression equation?
15.4 A large corporation is interested in predicting a measure of job satisfaction among its em-
ployees. They have collected data on 15 employees who each supplied information on job
satisfaction, level of responsibility, number of people supervised, rating of working envi-
ronment, and years of service. The data follow:
Satisfaction: 223355666788899
Responsibility: 423628458896379
No. Supervised: 534748659893699
Environment: 117358556472879
Years of Service: 575336327355881
Exhibit 15.6 is an abbreviated form of the printout.
a. Write out the regression equation using all five predictors.
b. What are the s?bibDEPENDENT VARIABLE ............... 1 SATIF
TOLERANCE.........................0.0100
ALL DATA CONSIDERED AS A SINGLE GROUP
MULTIPLE R 0.6974 STD. ERROR OF EST. 2.0572
MULTIPLE R-SQUARE 0.4864
ANALYSIS OF VARIANCE
SUM OF SQUARES DF MEAN SQUARE F RATIO P(TAIL)
REGRESSION 40.078 4 10.020 2.367 0.12267
RESIDUAL 42.322 10 4.232
STD. STD. REG
VARIABLE COEFFICIENT ERROR COEFF T P(2 TAIL) TOLERANCE
INTERCEPT 1.66926
RESPON 2 0.60516 0.428 0.624 1.414 0.188 0.263940
NUMSUP 3 – 0.33399 0.537 – 0.311 – 0.622 0.548 0.205947
ENVIR 4 0.48552 0.276 0.514 1.758 0.109 0.600837
YRS 5 0.07023 0.262 0.063 0.268 0.794 0.919492Exhibit 15.6 Printout for regression analysis of data in Exercise 15.415.5 Refer to Exercise 15.4.
a. Which variable has the largest semipartial correlation with the criterion, partialling out
the other variables?
b. The overall Fin Exercise 15.4 is not significant, yet Environment correlates signifi-
cantly (r 5 .58) with Y. How is this possible?