Chapter 3.2, Problem 78E

To determine

To find: the residual of child

Answer to Problem 78E

The child's residual is -3.2cm

Explanation of Solution

Given:

  $\widehat{y}=6.4+0.93x$

1. -3.2 cm.
2. -2.2 cm.
3. -1.3 cm.
4. 3.2 cm
5. 62.2 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).

It is given that one child in Mumbai study had height 59 cm and arm span 60 cm.

That is, the observed height of one child is 59 cm.

That is, $Y=59cm$

The predicted height, $\widehat{Y}$ for 60 cm of arm span is calculated as follows:

  $\begin{array}{l}\widehat{y}=6.4+0.93x\\ =6.4+0.93\times 60\\ =62.2\text{cm}\end{array}$

The residual of the child height is calculated as follows:

  $\begin{array}{l}\text{Residual = Observed height - Predicted height}\\ Y\text{-}\widehat{Y}\\ =59-62.2\\ =-3.2\text{ cm}\end{array}$

Conclusion: Hence, the child's residual is -3.2cm (option (a))