1. Suppose the Bank of Delaware would like to develop a regression model to predict a person's credit score based on his or her age, weekly income, and the type of primary residence (whether he or she owns or rents his or her primary residence). The file "Bank of Delaware 1" provides these data for 60 customers. As demonstrated in the lecture, please make a subset data of size 50 and perform your statistical analysis for the subset data. Please note that the subset data should be a random sample of the given data.

(a) State the multiple linear regression model in context of the problem.

(b) Is the multiple linear regression model in part (a) significant? Show details of the hypothesis test. Use = 0.06.

(c) Is age a significant predictor? Show details of the hypothesis test. Use = 0.06.

(d) Write down the estimated multiple linear regression equations for the two types of primary residences separately.

(e) Provide the detailed interpretations of the coefficients of the slopes of the regression equation in the context of the problem. 1

(f) Compute a 94% confidence interval for the coefficient of age using computer software. Interpret it in the context of the problem. Please verify your result manually. This will help you for your final exam.

(g) Use your estimated regression equation to predict the average credit score for a 38-year-old person who earns $1,200 per week, and owns his or her residence.

Credit ScoreIncome ($)AgeResidenceEducation

51864438RentHigh school

533103329RentHigh school

561107333OwnHigh school

564110046OwnBachelor

57353840RentBachelor

57878134OwnHigh school

591140356OwnBachelor

594156639RentGraduate

597125850RentHigh school

600115935RentHigh school

604123136OwnHigh school

60498537RentBachelor

607126041OwnBachelor

614111445RentHigh school

615111244RentBachelor

617117757OwnHigh school

617120139RentBachelor

621186734RentBachelor

623149444OwnBachelor

62562533RentBachelor

625156041OwnHigh school

633136537OwnHigh school

63668341OwnBachelor

63979456OwnBachelor

642125242OwnHigh school

643109949OwnBachelor

64492453RentBachelor

650132343OwnBachelor

654162053RentGraduate

65591543RentBachelor

65799843OwnGraduate

659158738OwnGraduate

66279644OwnHigh school

669140539RentBachelor

675147944RentBachelor

675141951RentBachelor

67588925OwnGraduate

67799445RentBachelor

678113533OwnBachelor

679181046OwnHigh school

687110546RentGraduate

688114047OwnBachelor

68871042OwnBachelor

693186949OwnBachelor

693112250RentBachelor

695121034OwnBachelor

695115851RentBachelor

699138544RentGraduate

699137651RentHigh school

702180252OwnHigh school

703169965RentBachelor

70981942OwnBachelor

712102543OwnBachelor

717156854OwnHigh school

731152155OwnBachelor

737129341OwnBachelor

749108834OwnBachelor

75390658OwnBachelor

784141859OwnBachelor

810139352OwnGraduate

2. Jersey Shore Realtors would like to develop a regression model to help it set weekly rental rates for beach properties during the summer season in New Jersey. The independent variables for this model are the number of bedrooms a property has, its age, the number of blocks away from the ocean it is, and the rental month (June, July, or August). These data can be found in the file "Jersey Shore Realtors 2". As demonstrated in the lecture, please create a subset data of size 78 and perform your statistical analysis for the subset data. Please note that the subset data should be a random sample of the given data.

(a) Is the number of bedrooms a significant predictor? Show details of the hypothesis test. Use = 0.5.

(b) Is the multiple linear regression model significant? Show details. Use = 0.05.

(c) Provide the detailed interpretations of the coefficients of the slopes of the regression model in the context of the problem.

(d) Use your estimated regression equation to predict the average weekly rental rate during the month of July for a three-bedroom house that is 10 years old and two blocks from the ocean.

Rental ($)BedroomsAgeBlocksMonth

8752123June

900342June

9002152June

10903131.5June

11753123June

12505112.5June

1400351.5June

1400482June

1500372June

1600362June

17004111.5June

1800473June

19004202June

2000453June

2000491.5June

2200541.5June

23006122.5June

25004102June

2600451June

30004142June

32005101.5June

3500491.5June

40005102June

4500491June

5000551.5June

70006140.5June

1475362July

19003181July

2250531.5July

23005112.5July

2525493July

2700382July

2700342.5July

28004112July

29004151.5July

30003131July

3000492.5July

34004132.5July

36004112July

3700461July

40004111July

4300591.5July

4700531.5July

49005111.5July

5000392July

52005161July

57005171.5July

6000632July

65005111July

7000491.5July

72006171July

76004121July

80005131July

90006210.5July

100005171July

129005100.5July

13002153August

17003102.5August

18003161.5August

19003112August

2000492.5August

2100463August

22004111.5August

2400451.5August

2800462August

29004132August

30004113August

32004112.5August

3400461August

3500582August

36005102August

37005141.5August

40004101.5August

41004202August

4250581August

4500521August

45005122August

45004132.5August

4800511.5August

5000592August

54006142August

57705101.5August

6000512August

78004121August

80005131.5August

90005160.5August

105006211.5August

12000420.5August