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 (coded as 1 = yes and 0 = no) to predict which customers are likely to purchase a new line of organic products. Data from a random sample of 100 loyalty program customers, organized and stored in Organic Food , show that 65 have purchased the organic products (coded 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 supermarket 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 and whether the customer subscribes to the supermarket chain's health/wellness e-newsletters to 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?