Using the regression model from Exercise 12-1,

(a) Find a 95% confidence interval for the coefficient of height.

(b) Find a 95% confidence interval for the mean percent of body fat for a man with a height of 72in and waist of 34in.

(c) Find a 95% prediction interval for the percent of body fat for a man with the same height and waist as in part (b).

(d) Which interval is wider, the confidence interval or the prediction interval? Explain briefly.

(e) Given your answer to part (c), do you believe that this is a useful model for predicting body fat? Explain briefly.

Exercise 12-1

Exercise 11.1 described a regression model between percent of body fat (%BF) as measured by immersion and BMI from a study on 250 male subjects. The researchers also measured 13 physical characteristics of each man, including his age (yrs), height (in), and waist size (in). A regression of percent of body fat with both height and waist as predictors shows the following computer output:

Residual standard error: 4.46 on 247 degrees of freedom Multiple R-squared: 0.7132, Adjusted R-squared: 0.7109 F-statistic: 307.1 on 2 and 247 DF, p-value: < 2.2e-16

Transcribed Image Text:

Estimate std. Error 7.68611 0.10994 0.07158 t-value Pr(>|t|) 0.687 (Intercept) Height Waist -3.10088 -0.60154 1.77309 -0.403 -5.472 24.770 1.09e-07 < 2e-16