Quantitative Methods

Oo 4,u,&arv t/.- 2 31 4 -)(y' flu; {tre quuho.J tn+d< r.t fiut'ch.gyU CHAPTER4 . REGRESSION MODELS

Use the data in Problcm 4-22 and develop a regrcs- sion modci to pledict sclling pricc bascd on the squarc tootage and numher of bcdrooms. Use this to predict the selling price of a 2.000-square-I'oot l.rouse with three bedroorns. Compare this rnodel with the models in Problem 4-22. Should the num- ber of bedroorns be included in the rnodel'J Whv or why not?

MPG HORSEPOWE,R WEIGHT

hv not'.'

/ 1-24,),Jsc thr data in Problem 4-22 and develop a rcgres- (----""-' sion rnodel to predict selling pricc based on the-

square fotrt.age, number of bedrooms, and age. Use this to predict the selling price of a 10-year-old.

37

37

3.+

t<

-1t

30

fa

26

26

25

22

20

2t

18

I8

16

16

69

66

(;3

90

99

6,1

9t

94

88

124

97

114

102

114

r ll

153

139

1.980

1,191

2.199

2.404

2.61I'

3,236

2.606

2.-580

) <r17 I Ql':r

) .a^ 1/

3.248

2.8t2

3,382

3.t97

4,380

4,036

2.000-sq uarc-1 oot l-rousc wi th thret bcdrooms. 4-25 The total e

l'actors. l-wo ol'these {actors are the number ol'beds in thc hospital and thc number of admissions. I)ata wcre collected on l4 hospitals. as shrrvn in the tbl- lowing table:

NT-IMBER

HO,SPTIAL OFBEDS ADMISSIONS TOTALEXPENSES

(100s) (N{ILLIONS)

I

2

-1

4

-5

6

1

8

()

10

11

t2

l3

14

2t-5

336

520

13-s

35

210

140

9t)

410

50

65

42

lt0 305

7l 160

230

43

9

155

53

6

r59

18

16

29

28

98

5l 121

1.57

21

t4

93

45

6

99

12

1l

l-5

2l

63

Find thc bcst rcgression modcl to predict the lotal cxpcnscs ol'a hospital. Discuss the accuracy of tl-ris n.rodel. Should both variables be included in the rnodel? Why or why not? A sample of 20 automobiles wa,s taken. and the miles per gallon (MPG). horsepower. and lotal *'eight were recorded. Dcvelop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop anorher rnodel with wei-cht as the independent variahle. Which of these two models is better? Explain.

4-27 Use thc data in Problent -tr-26 to develop a multiple lincar legression modcl. How docs this conrparc with each of the rnodels in Ilroblem 4-26'l

4-28 Use the data in Problem 4-26 to lintl the best qua- dratic regression modcl. (There is morc than onc to consider.) How docs this compare to the rnodels in Problems 4-26 and 1-27?

4-29 A sample of nirrc public universities and nint prilatc- lrniversities was taken. The total cost tbr the year (in- cluding room and board) and the median SAT score (maximum total is 2400) at each school were recorded. It was felt that schools with higher rnedian SAT scores would have a better reputation and would charge more tuition as a result of that. The data are in the follow- ing tablc. Use regression to help answer thc lollow- ing qucstions bascd on this samplc data. Do schools with higher SAT scores charge more in tuition and fees'l Are private schools more expensivc than pub- lic schools when SAT scores are taken into consider- ation? Discuss how accurate you believe these results are using infomration related to the regression models.

CATEGORY TOTAL COST ($) MEDIAN SAT

-$: a-26

MPG HORSEPOWER WEIGHT

1,84,1

r.998

1.152

Puhlic

Public

Public

Public

Puhlic

Public

Pubtic

Public

21.700

l -5,600

16,900

1-5,400

23,1 00

21,,100

16.500

23,500

r 990

I 620

1 810

1 540

15,10

I 600

l 560

189t)

44

40

67

50

62

(Continuetl. ott trcxt pdga)

Quantitative Analysis for Management, Twelfth Edition, by Barry Render, Ralph M. Stair, Michael E. Hanna, and Trevor S. Hale. Published by prentice Hail. Copyright @ 201 5 by Pearson Education, lnc.