Question

Ideal proportions Refer to Exercise 10.

(a) What height would you predict for a student with an arm span of 76 inches? Show your work.

(b) About how far off do you expect the prediction in part (a) to be from the student's actual height? Justify your answer.

Short answer

a) 75.41892 inches.

b)$1.613$

Step-by-step solution

Part(a) Step 1: Given Information

Need to find What height would you predict for a student with an arm span of 76 inches.

Part(a) Step 2: Explanation

The estimates a and b are given in the column of "Coef":

$\hat{y}=11.547+0.84042x$

Replace x by 5 and evaluate:

$$\begin{gathered} y=11.547+0.84042\left(76\right) \\ =75.41892 \end{gathered}$$

This means that we predict that the student will be $75.41892$inches tall.

Part(a) Step 1: Given Information

Given:

$s=1.613$

Part(b) Step 2: Explanation

Given:

$s=1.613$

The expected error made when making predictions is given by $\sigma$, which is estimated by s. Thus we expect that the prediction will be off by 1.613 on average.