Chapter 1.4, Problem 28E

a.

To determine

To find: value of that the equation in Example 3 predicts.

Answer to Problem 28E

41170

Explanation of Solution

Given information:

The equation in example 3 is as follows:

  $y=939x+10183$

The prediction value of number of years since 1980 (i.e. x ) is 33.

Calculation:

Substitute $x=33$ in the given equation and evaluate y as shown below.

  $\begin{array}{c}y=939\left(33\right)+10183\\ =30987+10183\\ =41170\end{array}$

Thus, the value of equation is 41170.

b.

To determine

To find: whether the average personal income and prediction value is same, and explain the difference.

Answer to Problem 28E

No, because only two points were used to make the prediction equation.

Explanation of Solution

Given information:

The equation in example 3 is as follows:

  $y=939x+10183$

The prediction value of number of years since 1980 (i.e. x ) is 33.

The value of equation (evaluated in part a.) is 41170.

Calculation:

The average personal income and prediction value will not be same because only two points were used to make the prediction equation. Thus, it may be conclude that many points lie off the line and there will be a difference between prediction and personal income.