Applied Statistics and Probability for Engineers

428 CHAPTER 12 MULTIPLE LINEAR REGRESSION

12-2 HYPOTHESIS TESTS IN MULTIPLE LINEAR REGRESSION

In multiple linear regression problems, certain tests of hypotheses about the model parameters

are useful in measuring model adequacy. In this section, we describe several important

hypothesis-testing procedures. As in the simple linear regression case, hypothesis testing

requires that the error terms iin the regression model are normally and independently dis-

tributed with mean zero and variance 2.

12-2.1 Test for Significance of Regression

The test for significance of regression is a test to determine whether a linear relationship exists

between the response variable yand a subset of the regressor variables x 1 , x 2 , p, xk. The

SHG Short-handed goals scored during the season.

PPGA Power play goals against.

PKPcT Penalty killing percentage. Measures a team’s

ability to prevent goals while its opponent is on a

power play. Opponent power play goals divided

by opponent’s opportunities.

SHGA Short-handed goals against. Fit a multiple linear

regression model relating wins to the other vari-

ables. Estimate 2 and find the standard errors of

the regression coefficients.

12-12. Consider the linear regression model

where and

(a) Write out the least squares normal equations for this model.

(b) Verify that the least squares estimate of the intercept in

this model is

(c) Suppose that we use as the response variable in the

model above. What effect will this have on the least

squares estimate of the intercept?

yiy

ˆ¿ 0 g yiny.

x 1 gx i 1 n x 2 gx i 2 n.

Yi¿ 0  11 xi 1 x 12  2 1 xi 2 x 22 i

Table 12-8

Team Wins Pts GF GA PPG PPcT SHG PPGA PKPcT SHGA

Chicago 47 104 338 268 86 27.2 4 71 76.6 6

Minnesota 40 96 321 290 91 26.4 17 67 80.7 20

Toronto 28 68 23 330 79 22.3 13 83 75 9

St. Louis 25 65 285 316 67 21.2 9 63 81.3 12

Detroit 21 57 263 344 37 19.3 7 80 72.6 9

Edmonton 47 106 424 315 86 29.3 22 89 77.5 6

Calgary 32 78 321 317 90 27 7 59 77.1 6

Vancouver 30 75 303 309 65 23.8 5 56 80.8 13

Winnipeg 33 74 311 333 78 23.6 10 67 72.8 7

Los Angeles 27 66 308 365 81 23.8 10 94 68.2 14

Philadelphia 49 106 326 240 60 21.6 15 61 82 7

NY Islanders 42 96 302 226 69 25.8 10 55 83.4 3

Washington 39 94 306 283 75 20.9 3 53 81.6 11

NY Rangers 35 80 306 287 71 22.4 12 75 76 8

New Jersey 17 48 230 338 66 21.9 74 78 73.5 10

Pittsburgh 18 45 257 394 81 22.6 3 110 72.2 15

Boston 50 110 327 228 67 22.2 8 53 80.7 6

Montreal 42 98 350 286 64 22.2 8 68 73.8 8

Buffalo 38 89 318 285 67 21.5 12 48 82.5 9

Quebec 34 80 343 336 61 20.7 6 92 73.6 6

Hartford 19 45 261 403 51 19.3 6 70 76.1 9

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