Chapter 4, Problem 10PT

a.

To determine

Find an equation for the best-fit line.

Answer to Problem 10PT

The equation of best fit line is $y=1.89x+23.57$ .

Explanation of Solution

Given information: The data where x represents the years experience and y represents the salary in thousands.

Years Experiencex	1	5	10	15	20
Salary (thousands of dollars) y	28	31	42	49	64

Calculation:

Formula used:

The equation for the regression line is given below.

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

Years Experiencex	1	5	10	15	20
Salary (thousands of dollars) y	28	31	42	49	64

Use a graphing calculator for above table ,

  $\begin{array}{l}\text{Sum}\text{of}x=51.\\ \text{Sum}\text{}\text{of}y=214.\\ \text{Mean}x=\mathrm{10.2.}\\ \text{Mean}y=\mathrm{42.8.}\\ \text{Sum}\text{of}\text{squares}(S{S}_x)=\mathrm{230.8.}\\ \text{Sum}\text{of}\text{products}(SP)=\mathrm{435.2.}\\ \text{Regression}\text{equation}y=ax+b.\\ a=SP/S{S}_x=435.2/230.8=\mathrm{1.88562.}\\ b=M_y-a{M}_x=42.8-(1.89\times 0.2)=\mathrm{23.56672.}\\ y=1.88562x+\mathrm{23.56672.}\end{array}$

So ,the equation of best fit line is $y=1.89x+23.57$

b.

To determine

Find the correlation coefficient and explain what is tells us about the relationship between experience and salary.

Answer to Problem 10PT

The correlation coefficient is 0.984420 which is very close to 1 tells that there is very strong relationship between experience and salary. That is if experience increases must increase the salary.

Explanation of Solution

Given information: The data where x represents the years experience and y represents the salary in thousands.

Years Experiencex	1	5	10	15	20
Salary (thousands of dollars) y	28	31	42	49	64

Calculation:

Formula used:

The equation for the regression line is given below.

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

Years Experiencex	1	5	10	15	20
Salary (thousands of dollars) y	28	31	42	49	64

Use a graphing calculator for above table ,

  $\begin{array}{l}\text{Sum}\text{of}x=51.\\ \text{Sum}\text{}\text{of}y=214.\\ \text{Mean}x=\mathrm{10.2.}\\ \text{Mean}y=\mathrm{42.8.}\\ \text{Sum}\text{of}\text{squares}(S{S}_x)=\mathrm{230.8.}\\ \text{Sum}\text{of}\text{products}(SP)=\mathrm{435.2.}\\ \text{Regression}\text{equation}y=ax+b.\\ a=SP/S{S}_x=435.2/230.8=\mathrm{1.88562.}\\ b=M_y-a{M}_x=42.8-(1.89\times 0.2)=\mathrm{23.56672.}\\ y=1.88562x+\mathrm{23.56672.}\end{array}$

So ,the equation of best fit line is $y=1.89x+23.57$

Using graph calculator,

The correlation coefficient is 0.984420 which is very close to 1 tells that there is very strong relationship between experience and salary. That is if experience increases must increase the salary.