Chapter 3.2, Problem 76E

To determine

To find: The residual of the child.

Answer to Problem 76E

The residual is $-3.2\text{ cm}$

Explanation of Solution

Given:

The regression line is $\widehat{y}=6.4+0.93x$

Formula used:

The formula to compute the residual is:

  $\text{Residual =}\left(y-\widehat{y}\right)$

Where,

  $y$ = Actual value

  $\widehat{y}$ = Predicted value

Calculation:

Here, predicted value can be computed as:

  $\begin{array}{c}\widehat{y}=6.4+0.93x\\ =6.4+0.93\left(60\right)\\ =62.2\end{array}$

Now, residual can be calculated as:

  $\begin{array}{c}\text{Residual =}\left(y-\widehat{y}\right)\\ =\left(59-62.2\right)\\ =-3.2\end{array}$

Thus, the residual is $-3.2\text{ cm}$

Hence, the correct option is (a).