Applied Statistics and Probability for Engineers

12-1 MULTIPLE LINEAR REGRESSION MODEL 419

to fit the regression model above to these data. The Xmatrix and yvector for this

model are

X y

The matrix is

and the vector is

The least squares estimates are found from Equation 12-13 as

ˆ 1 X¿X 2 ^1 X¿y

X¿y£

11 p 1

28 p 5

50 110 p 400

§≥

9.95

24.45

o

21.15

¥£

725.82

8,008.37

274,811.31

§

X¿y

X¿X£

11 p 1

28 p 5

50 110 p 400

§ ̨≥

12 50

1 8 110

ooo

1 5 400

¥£

25 206 8,294

206 2,396 77,177

8,294 77,177 3,531,848

§

X¿X

9.95

24.45

31.75

35.00

25.02

16.86

14.38

9.60

24.35

27.50

17.08

37.00

41.95

11.66

21.65

17.89

69.00

10.30

34.93

46.59

44.88

54.12

56.63

22.13

21.15

1250

1 8 110

1 11 120

1 10 550

1 8 295

1 4 200

1 2 375

1252

1 9 100

1 8 300

1 4 412

1 11 400

1 12 500

1 2 360

1 4 205

1 4 400

1 20 600

1 1 585

1 10 540

1 15 250

1 15 290

1 16 510

1 17 590

1 6 100

1 5 400

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