Chapter 4.6, Problem 21PFA

To determine

To find which of the following best predicts the fee in the year 2020.

Answer to Problem 21PFA

C$y=26.5(\$)$ .

Explanation of Solution

Given information: The table shows the canceled check fee for a bank from 2013 to

2016.

Years	0	1	2	3
Fee($)	5	10	10	15

Formula used:

The equation for the regression line or line of best fit is given below.

  $\begin{array}{c}y=ax+b.\\ \text{Where},a=\frac{n{\displaystyle \sum xy-({\displaystyle \sum x)({\displaystyle \sum y)}}}}{n{\displaystyle \sum x^2-({\displaystyle \sum x{)}^2}}}.\\ b=\frac{{\displaystyle \sum y-a{\displaystyle \sum x}}}{n}.\\ \text{Where, }\text{n=number}\text{of}\text{observations}.\end{array}$

Calculation:

Let x be the number of years since 2013and y represents the canceled check fee($).

Years x	0	1	2	3
Fee($) y	5	10	10	15

Use a graphing calculator for above table ,

Line of Best Fit ,

  $\begin{array}{l}y=3x+5.5.\\ \text{Intercept}=5.5.\\ \text{Slope}=3.\end{array}$

To estimate thebest predicts the fee in 2020, evaluate the Line of Best fit for x = 7 because 2020 is 7 years after 2013.

  $\begin{array}{l}y=3x+5.5.\\ \text{putting}x=7.\\ y=3\times 7+5.5.\\ y=21+5.5.\\ y=26.5(\$).\end{array}$