Logistic regression Excel and Minitab

Question1.

A researcher is studying how predictors, such as GRE (Graduate Record Exam scores), GPA(grade point average) and Prestige (prestige of the undergraduate institution; a value between1 (lowest) and 4 (highest)), will affect admission into graduate school. The response variable iscodedasAdmit=1ifthestudentisadmitted and Admit=0ifnot.

a) Use Minitab to develop and state the estimated logistic regression equation to predictAdmit by GRE, GPA and Prestige. (Assume for now that Prestige is a quantitativevariable.)

b) Testforoverallsignificance atthe 0.05level.

c) Whichofthepredictorsarestatisticallysignificantatthe0.05level?

d) Use hand-calculations based on the estimated logistic regression equation in part a) toestimate the probability of admission for a student from an institution of prestige level 3if the student has a score of 660 on their GRE and a 3.9 GPA. Verify your hand-calculationsusing Minitab.

e) FindtheestimatedoddsratiofortheGPAandinterpretit.

f) FindtheestimatedoddsratioforPrestigeandinterpretit.

g) Illustrate the odds ratio by comparing the odds in favour of being admitted into gradschool for a person with 660 GRE and 3.90 GPA from a college with prestige level 3 to aperson with the same GRA and GPA from a college with prestige level 2 and anotherwith prestigelevel4.

h) Forallthreepersonscomputethe probability ofbeingadmitted intogradschool.

i) Repeat parts a) and b) but now assume that Prestige is a categorical variable. (You canfit the model without computing indicator variables by declaring Prestige as acategoricalpredictor.)

Question2.

A marketing consultant for a cereal company investigates the effectiveness of a TVadvertisement for a new cereal product. The consultant shows the advertisement in a specificcommunity for one week. Then the consultant randomly samples adults as they leave a localsupermarket to ask whether they saw the advertisement (0 = no, 1 = yes) and bought the newcereal (0 = no, 1 = yes). The consultant also asks adults what their annual household income is(in thousand of dollars). Binary logistic regression is used to determine how the income levelandseeingthe TVadarerelatedtowhetherornottheadultssampledboughtthe cereal.

a. Using Minitab, develop and state the estimated logistic regression equation to predictwhether a customerwillbuythecerealornot.

b. For each predictor variable, determine whether it is significant or not. Use a 0.05 levelofsignificance.

c. Suppose a customer earns $51k annually and watched the ad. What is the estimatedprobabilitythecustomerwillbuythecereal?

d. Whatarethe estimatedoddsinfavour ofthecustomerinpart(c)buyingthe cereal?

e. FindtheestimatedoddsratioforthepredictorViewAdandinterpretit.

Bought

Income

ViewAd

0

37

0

1

47

1

0

47

0

0

49

0

1

59

1

0

13

1

0

51

0

0

38

0

0

60

1

1

48

1

0

17

0

0

60

0

0

38

1

0

24

0

0

15

0

1

59

0

0

28

0

0

36

0

0

10

1

0

46

0

1

55

1

0

37

1

1

13

1

0

55

0

1

34

0

0

24

0

0

19

0

0

55

1

0

53

1

1

57

1

0

30

1

0

53

0

0

60

1

1

51

1

1

23

1

0

53

1

0

43

0

0

35

1

0

33

1

0

30

0

0

34

0

0

43

0

0

36

0

1

44

1

0

60

1

0

56

0

0

60

1

1

11

0

0

33

0

1

22

0

1

45

1

1

55

0

1

60

1

0

20

0

0

15

1

0

10

0

1

44

1

0

25

0

0

15

1

1

38

1

0

10

0

0

15

1

1

42

1

1

33

0

0

24

0

0

15

1

0

24

1

1

52

0

0

21

0

0

21

0

1

30

1

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