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Binary Logistic Regression: Bought versus Income, ViewAd

Regression Equation

P(1)= expl/(1-exp

Y = -3.623-0.0491 Income - 0.0 ViewAd No-1.605 ViewAd Yes

Coefficients

Coef SE Coef VIF

Term

Constant -3.623 0.967

Income 0.0491 0.0207 1.01

ViewAd

1.605 0617 1.01

Odds Ratios for Continuous Predictors

Odds Ratio 95% CI

Income 1.0503 (1.0086, 1.0937)

Odds Ratios for Categorical Predictors

Level A Level B Odds Ratio 95% CI

ViewAd

Yes No

49783 (1.4855, 16.6835)

Odds ratio for level A relative to level

A marketing consultant for a cereal company is investigating the effectiveness of a TV advertisement for a breakfast cereal. The

consultant shows the advertisement in a specific community for one month. Then, she randomly samples shoppers as they leave a

local supermarket to ask whether they viewed the Ad and whether they Bought the new cereal. The consultant also asks the

subjects their annual household Income ($1000). Data is recorded in Minitab and a logistic regression is fit. The output is above.

a. Based on this model, for a person with income of $45,000 who viewed the ad, what is the

predicted probability that they will buy the cereal?

b. Based on this model, for a person with income of $45,000 who did not view the ad, what is the

predicted probability that they will buy the cereal?

c.

To get the odds of buying the cereal for the person in part a, we must multiply the odds for the

person in part b by what number?

d. Interpret the slopes of the predictors.

e. Which predictor(s) is/are significant at the 5% level? Briefly explain your answer.

Fig: 1