Chapter 3.2, Problem 75E

To determine

To find: height of a child with an arm span of 100cm

Answer to Problem 75E

The predicted height of the child is (b) 99.4 cm

Explanation of Solution

Given:

  $\widehat{y}=6.4+0.93x$

1. 106.4 cm
2. 99.4 cm
3. 93 cm.
4. 15.7 cm.
5. 7.33 cm.

Calculation:

Measurements on young children in Mumbai, India, found a least-squares line for predicting height Y from arm span X.

  $\widehat{y}=6.4+0.93x$

Measurements are in centimeters (cm).

We are supposed to find the predicted height of a child with an arm span of 100cm.

That is, $x=100\text{cm}$

Then, the predicted height of child is calculated as follows:

  $\begin{array}{l}\widehat{y}=6.4+0.93x\\ =6.4+0.93\times 100\\ =99.4\text{ cm}\end{array}$

The predicted height of a child with an arm span of 100 cm is about 99.4 cm.

Conclusion:

The predicted height of a child with an arm span of 100 cm is about 99.4 cm.