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A person's muscle mass is expected to decrease with age. To explore this relationship in women, a nutritionist randomly selected 16 women from each 10-year age group, beginning with age 40 and ending with age 79. The variables include X = age and Y = measure of muscle mass. a) Fit and report the results for the following regression model: Y, = Bo + ß Xi + ß2 X7, + b) Does the quadratic regression function appear to be a good fit here? Find R2. Conduct an overall F-test of the model using a-0.05. State the alternatives, decision rule, and conclusion. c) Estimate the mean muscle mass for women aged 48 years by reporting a 95% confidence interval. Interpret your interval. d) Predict the muscle mass for a woman whose age is 48 years by reporting a 95% prediction interval. Interpret your interval. Test whether the quadratic term can be dropped from the regression model; use a- 0.05. State the alternatives, decision rule, and conclusion.

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