Chapter 14, Problem 60PS

A local supermarket manager wants to use two independent variables, customer age (in years) and whether the customer subscribes to the supermarket chain’s health/wellness e-newsletters (codes as $\text{1}=\text{yes,}\text{and 0}=\text{no}).$ to predict which customer are likely to purchase a new line of organic product. Data from a random sample of 100 loyalty program customers, organized and stored in OrganicFood, show that 65 have purchased the organic products (codes as 1) and 35 have not coded as 0).

a. Develop a logistic regression model to predict the probability that a customer purchases the organic products, based on age and whether the customer subscribes to the supermarket chain’s health/wellness e-newsletters.

b. Explain the meaning of the regression coefficients in the model in (a).

c. Predict the probability of purchasing the organic products for a 35-year-old customer who subscribes to the submarket chain’s health/wellness e-newsletters.

d. At the 0.05 level of significance, is there evidence that a logistic regression model that uses customer age the whether the customer subscribes to the supermarket chain’s health/wellness e-newsletters to the predict the probability of purchasing the organic products is a good fitting model?

e. At the 0.05 level of significance, is there evidence that customer age and whether the customer subscribes to the supermarket chain’s health/wellness e -newsletters each make a significant contribution to the logistic model?

f. What conclusions can you reach about which variables are affecting purchase of organic foods?