Chapter 13.4, Problem 39E

In Exercise 13.19, we considered a regression of y = Oxygen consumption on x = Time spent exercising. Summary quantities given there yield

$\begin{array}{l}n=20\bar{x}=2.50S_{xx}=25\\ b=97.26a=592.10s_e=16.486\end{array}$

1. a. Calculate $s_{a+b\left(2.0\right)}$, the estimate standard deviation of the statistic $a+b\left(2.0\right)$.
2. b. Without any further calculation, what is $s_{a+b\left(3.0\right)}$ and what reasoning did you use to obtain it?
3. c. Calculate the estimated standard deviation of the statistic $a+b\left(2.8\right)$.
4. d. For what value x* is the estimated standard deviation of a + bx*smallest, and why?

13.19 An experiment to study the relationship between x = Time spent exercising (minutes) and y = Amount of oxygen consumed during the exercise period resulted in the following summary statistics.

$\begin{array}{l}n=20\Sigma x=50\Sigma y=16,705\Sigma x^2=150\\ \Sigma y^2=14,194,231\Sigma xy=44,194\end{array}$

1. a. Estimate the slope and y intercept of the population regression line.
2. b. One sample observation on oxygen usage was 757 for a 2-minute exercise period. What amount of oxygen consumption is predicted for this exercise period, and what is the corresponding residual?
3. c. Calculate a 99% confidence interval for the average change in oxygen consumption associated with a 1-minute increase in exercise time.