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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