Fou X IEPr X In MA X In MA X In MA X Exp X M Nev X alll STA X 3 hw x hwe x UF App X * 313 X C 8.4. X C Pro X C Ple: X + V X -> C o users.stat.ufl.edu/~winner/sta4211/ALSM_5Ed_Kutner.pdf E Applied linear statistical models.djvu 369 / 1415 - 150% + data." a. Comment on the criticism. b. Might R2 defined in (6.42) be more appropriate than R2 as a descriptive measure here?' *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. 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 R2 369 b. Test whether or not there is a regression relation; use a = .05. State the alternatives, decision rule, and conclusion. c. -Estimate the mean muscle mass for women aged 48 years; use a 95 percent confidence interval. Interpret your interval. d. Predict the muscle mass for a woman whose age is 48 years; use a 95 percent prediction interval. Interpret your interval. e. Test whether the quadratic term can be dropped from the regression model; use a = .05. State the alternatives, decision rule, and conclusion. 370 f. Express the fitted regression function obtained in part (a) in terms of the original variable X. g. Calculate the coefficient of simple correlation between X and X2 and between x and x2. Is the use of a centered variable helpful here? $8.5. Refer to Muscle mass Problems 1.27 and 8.4. a. Obtain the residuals from the fit in 8.4a and plot them against Y and against x on separate graphs. Also prepare a normal probability plot. Interpret your plots. b. Test formally for lack of fit of the quadratic regression function; use o = .05. State the alternatives, decision rule, and conclusion. What assumptions did you make implicitly in 371 this test? 7:47 PM Type here to search 56F Sunny ENG 4/11/2022IEProject X Expositi X will STAT52 x 5 hw9.pd x & hw8.pd x UF Applied X UF Applied X * 313 E1 X PS4 Che X C 8.4. Ref x C Problen x C Please | X + V X > C a users.stat.ufl.edu/~winner/sta4211/ALSM_5Ed_Kutner.pdf A E Applied linear statistical models.djvu 60 / 1415 - 150% + 1.25. Refer to Airfreight breakage Problem 1.21. a. Obtain the residual for the first case. What is its relation to &,? b. Compute Le, and MSE. What is estimated by MSE? 57 1.26. Refer to Plastic hardness Problem 1.22. a. Obtain the residuals e;. Do they sum to zero in accord with (1.17)? b. Estimate of and o. In what units is o expressed? $1.27. Muscle mass. A person's muscle mass is expected to decrease with age. To explore this rela- tionship in women, a nutritionist randomly selected 15 women from each 10-year age group, beginning with age 40 and ending with age 79. The results follow; X is age, and Y is a measure of muscle mass. Assume that first-order regression model (1.1) is appropriate. 58 i: 2 3 . . . 58 59 60 X/: 43 41 47 76 72 76 Y: 106 106 97 . . . 56 70 74 a. Obtain the estimated regression function. Plot the estimated regression function and the data. Does a linear regression function appear to give a good fit here? Does your plot support the anticipation that muscle mass decreases with age? b. Obtain the following: (1) a point estimate of the difference in the mean muscle mass for 59 women differing in age by one year, (2) a point estimate of the mean muscle mass for women aged X = 60 years, (3) the value of the residual for the eighth case, (4) a point estimate of o2. Chapter 1 Linear Regression with One Predictor Variable 37 60 8:25 PM Type here to search 56.F Sunny ENG 4/11/2022