In Problem 15-48, you were asked to use best subsets stepwise regression to establish the relationship between body fat and the independent variables weight, abdomen circumference, and thigh circumference based on data in the file Bodyfat . This is an extension of that exercise.
a. Construct an estimate of the regression equation using the same variables.
b. Produce the appropriate residual plots to determine if the linear function is the appropriate regression function for this data set.
c. Use a residual plot to determine if the residuals have a constant variance.
d. Produce the appropriate residual plot to determine if the residuals are independent. Assume the data were extracted in the order listed.
e. Construct a probability plot to determine if the error terms are normally distributed.
In exercise
A variety of sources suggest that individuals assess their health, at least in part, by estimating their percentage of body fat. A widely accepted measure of body fat uses an underwater weighing technique. There are, however, more convenient methods using only a scale and a measuring tape. An article in the Journal of Statistics Education by Roger W. Johnson explored regression models to predict body fat. The file titled Bodyfat lists a portion of the data presented in the cited article.
a. Use best subsets stepwise regression to establish the relationship between body fat and the variables in the specified file.
b. Predict the body fat of an individual whose age is 21, weight is 170 pounds, height is 70 inches, chest circumference is 100 centimeters, abdomen is 90 centimeters, hip is 105 centimeters, and thigh is 60 centimeters around.