In the article “Tri-ponderal mass index vs body mass index in estimating body fat during adolescence” published in JAMA Pediatrics (Peterson, et al., 2017), the authors reported the fitted multiple regression model relating body fat percentage for men and boys to tri-ponderal mass index (???? = 2285). The fitted model reported isˆBF% = 18.472

+ 4.226TMI − 0.064TMI2 (????2 = 0.64) where BF% is a body fat percentage and TMI is tri-ponderal mass index.

(a) Estimate the mean value of BF% for a tri-ponderal value of TMI=20.

(b) If the estimated standard error of the estimated mean in part

(a) is ???????? = 1.54, compute a 95% confidence interval for the mean value of BF% for TMI=20.

(c) Predict the value of BF% for a male with a value of TMI=20.

(d) If the ???????? = 2.13, compute a 95% prediction interval for the value of BF% for a male with TMI=20.