Chapter 4.6, Problem 19PPS

To determine

To find an equation for the best-fit line that models the data where x represents the number of years since 2014 and y represents the number of yo-yo sold in thousands using graphing calculator.

Answer to Problem 19PPS

A $y=-1.26x+9.09$ .

Explanation of Solution

Given information: The table shows yo-yo sold for a company over a 4-year period.

Years	2014	2015	2016	2017
Yo-Yos Sold y (thousands)	9.7	7.1	6.2	5.8

Formula used:

The equation for the best fit line 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 2014 and y represents the number of yo-yo sold in

thousands.

Years x	0	1	2	3
Yo-Yos Sold y (thousands)	9.7	7.1	6.2	5.8

Use a graphing calculator for above table ,

Line of Best Fit

  $\begin{array}{l}y=-1.26x+\mathrm{9.09.}\\ \text{Intercept}=9.09.\\ \text{Slope}=-1.26.\end{array}$