Baruch College, STA 9700 HW 8, Page 1 *8.4. Refer to Muscle mass Problem 1.27. Second-order regression model (8.2) with independent normal error terms is expected to be appropriate. *8.5. a. o 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?. Test whether or not there is a regression relation; use & = .05. State the alternatives, decision rule, and conclusion. Estimate the mean muscle mass for women aged 48 years; use a 95 percent confidence interval. Interpret your interval. Predict the muscle mass for a woman whose age is 48 years; use a 95 percent prediction interval. Interpret your interval. Test whether the quadratic term can be dropped from the regression model; use & = .05. State the alternatives, decision rule, and conclusion. Express the fitted regression function obtained in part (a) in terms of the original variable X . Calculate the coefficient of simple correlation between X and X2 and between x and x. Is the use of a centered variable helpful here? Refer to Muscle mass Problems 1.27 and 8.4. a. Obtain the residuals from the fit in 8.4a and plot them against and against x on separate graphs. Also prepare a normal probability plot. Interpret your plots. Test formally for lack of fit of the quadratic regression function; use =.05. State the alternatives, decision rule, and conclusion. What assumptions did you make implicitly in this test? Fit third-order model (8.6) and test whether ornot 81, = 0; use o = .05. State the alternatives, decision rule, and conclusion. Is your conclusion consistent with your finding in part (b)