The marketing manager for a nationally franchised lawn service company developed a logistic regression model to predict which suburban homeowners would purchase a lawn service. The model included the following predictor variables: Income, in thousands of dollars, Lawn Size, in thousands of square feet, Attitude, attitude toward outdoor recreational activities (0 = unfavorable, 1 = favorable), Teenager, number of teenagers in the household and Age, age of the head of the homeowner. The fitted logistic regression model is

Question

The marketing manager for a nationally franchised lawn service company developed a logistic regression model to predict which suburban homeowners would purchase a lawn service. The model included the following predictor variables: Income, in thousands of dollars, Lawn Size, in thousands of square feet, Attitude, attitude toward outdoor recreational activities (0 = unfavorable, 1 = favorable), Teenager, number of teenagers in the household and Age, age of the head of the homeowner. The fitted logistic regression model is

Ln(estimated odds of purchase) = -70.49 + 0.2868 Income + 1.0647 LawnSize – 12.744 Attitude – 0.200 Teenager + 1.0792 Age

Consider the case of a 48-year-old homeowner with a family income of $100,000, a lawn size of 5,000 square feet, a positive attitude toward outdoor recreation, and two teenagers in the household.

What are the estimated odds that this homeowner will purchase a lawn service?
What is the estimated probability that this homeowner will purchase a lawn service?

Answer 1

To calculate the estimated odds that this homeowner will purchase a lawn service, we can plug the values of the predictor variables into the logistic regression equation:

Ln(estimated odds of purchase) = -70.49 + 0.2868(100) + 1.0647(5) - 12.744(1) - 0.200(2) + 1.0792(48)

Simplifying the equation:

Ln(estimated odds of purchase) = -70.49 + 28.68 + 5.3235 - 12.744 - 0.400 + 51.8736

Ln(estimated odds of purchase) = 2.2376

To calculate the estimated probability that this homeowner will purchase a lawn service, we can use the equation:

Probability of purchase = exp(Ln(estimated odds of purchase)) / (1 + exp(Ln(estimated odds of purchase)))

Substituting the value of Ln(estimated odds of purchase) that we calculated above:

Probability of purchase = exp(2.2376) / (1 + exp(2.2376))

Calculating the probability:

Probability of purchase = 0.9031

Therefore, the estimated odds that this homeowner will purchase a lawn service are approximately 2.2376, and the estimated probability is approximately 0.9031.