1) A study was conducted attempting to relate home ownership to family income. Twenty households were selected and family income was estimated, along with information concerning home ownership (y = 1 indicates yes and y = 0 indicates no). The data are shown below.

(a) Fit a logistic regression model to the response variable y. Use a simple linear regression model as the structure for the linear predictor.

(b) Is the logistic regression model in part (a) adequate?

(c) Provide an interpretation of the parameter 1 in this model.

2. A study was performed to investigate new automobile purchases. A sample of 20 families was selected. Each family was surveyed to determine the age of their oldest vehicle and their total family income. A follow-up survey was conducted six months later to determine if they had actually purchased a new vehicle during that time period(y = 1 indicates yes and y = 0 indicates no). The data from this study are shown in the following table.

(a) Fit a logistic regression model to the data.

(b) Is the logistic regression model in part (a) adequate?

(c) Interpret the model coecients 1 and 2.

(d) What is the estimated probability that a family with an income of $45,000 and a car that is ve years old will purchase a new vehicle in the next six months?

(e) Expand the linear predictor to include an interaction term. Is there any evidence that this term
is required in the model?

3. The World Health Organization de nes obesity in adults as having a body mass index (BMI) higher than 30. Of the 250 men in the study mentioned in Exercise 11-1, 23 are by this de nition obese. How good is waist (size in inches) as a predictor of obesity? A logistic regression model was t to the data log(p1 p) = 41:828 + 0:9864 waist; where p is the probability of being classi ed as obese.

(a) Does the probability of being classi ed as obese increase or decrease as a function of waist size? Explain.

(b) What is the estimated probability of being classi ed as obese for a man with waist size of 36 inches?

(c) What is the estimated probability of being classi ed as obese for a man with waist size of 42 inches?

(d) What is the estimated probability of being classi ed as obese for a man with waist size of 48 inches?

(e) Make a plot of the estimated probability of being classi ed as obese as a function of waist size.