8.6. Steroid level. An endocrinologist was interested in exploring the relationship between the level of a steroid (Y) and age (X) in healthy female subjects whose ages ranged from 8 to 25 years. She collected a sample of 27 healthy females in this age range. The data are given below: 2 3 25 26 27 X;: 23 19 25 13 14 18 YA: 27.1 22.1 21.9 12.8 20.8 20.6 a. Fit regression model (8.2). Plot the fitted regression function and the data. Does the quadratic regression function appear to be a good fit here? Find R. b. Test whether or not there is a regression relation; use a = .01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? c. Obtain joint interval estimates for the mean steroid level of females aged 10, 15, and 20, respectively. Use the most efficient simultaneous estimation procedure and a 99 percent family confidence coefficient. Interpret your intervals. d. Predict the steroid levels of females aged 15 using a 99 percent prediction interval. Interpret your interval. e. Test whether the quadratic term can be dropped from the model; use o =.01. State the alternatives, decision rule, and conclusion. f. Express the fitted regression function obtained in part (a) in terms of the original variable X.