Problem

Sales of Riding Mowers. A company that manufactures riding mowers wants to identify the best sales prospects for an intensive sales campaign. In particular, the manufacturer is interested in classifying households as prospective owners or nonowners on the basis of Income (in $1000s) and Lot Size (in 1000 ft2). The marketing expert looked at a random sample of 24 households, given in the file RidingMowers.csv. Use all the data to fit a logistic regression of ownership on the two predictors.

a. What percentage of households in the study were owners of a riding mower?

b. Create a scatter plot of Income vs. Lot Size using color or symbol to distinguish owners from nonowners. From the scatter plot, which class seems to have a higher average income, owners or nonowners?

c. Among nonowners, what is the percentage of households classified correctly?

d. To increase the percentage of correctly classified nonowners, should the cutoff probability be increased or decreased?

e. What are the odds that a household with a $60K income and a lot size of 20,000 ft2 is an owner?

f. What is the classification of a household with a $60K income and a lot size of 20,000 ft2? Use cutoff = 0.5. g. What is the minimum income that a household with 16,000 ft2 lot size should have before it is classified as an owner?