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: . i: Xi: Yi: 23 27.1 2 19 22.1 3 25 21.9 25 13 12.8 26 14 20.8 27 18 20.6 a. Fit regression model (8.2). Plotthe fitted regression function and the data. Does the qUadratic regression function appear to be a good fit here? Find R2. .. '0 b. Test whether or not there is a regression relation; usea = .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 simultllpeous estimation procedure and a 99 family confidence coefficient. Interpret your intervals. d. Predict the steroid levels of females aged IS using a 99 percent prediction interval. Interpret your interval. e. Test whether the quadratic term can be dropped from the model; use a = .01. State the alternatives, decision mle, and conclusion. f. Express the fitted regression function obtained in part (a) in terms ofthe original variable X.