Chapter ISG, Problem 4.6STP

a.

To determine

To find: a linear regression modal that fits the data using graphical calculator.

Answer to Problem 4.6STP

The equation for the linear regression modal is $y=5.03267x-46.94589$ .

Explanation of Solution

Given information: The table shows the number of people who entered a store and the

total sales each hour.

Number of people	42	17	26	50	57	42	39	44	64	31
Total sales	155	33	109	240	237	129	136	189	271	105

Formula used:

The equation for the linear regression modal 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:

Using the graphing calculator the equation for the linear regression modal on above table data is:

  $\begin{array}{l}\text{Sum}\text{of}x=412.\\ \text{Sum}\text{}\text{of}y=1604.\\ \text{Mean}x=\mathrm{41.2.}\\ \text{Mean}y=\mathrm{160.4.}\\ \text{Sum}\text{of}\text{squares}(S{S}_x)=\mathrm{1781.6.}\\ \text{Sum}\text{of}\text{products}(SP)=\mathrm{8966.2.}\\ \text{Linear}\text{equation}y=ax+b.\\ a=SP/S{S}_x=8966.2/1781.6=\mathrm{5.03267.}\\ b=M_y-a{M}_x=160.4-(5.03\times 41.2)=-\mathrm{46.94589.}\\ y=5.03267x-\mathrm{46.94589.}\end{array}$

The equation for the linear regression modal is $y=5.03267x-46.94589$ .

b.

To determine

To find: the r value for your regression mode and what does this r value mean.

Answer to Problem 4.6STP

The r value means “correlation coefficient” of the regression modal.

r = 0.96153463534215

Explanation of Solution

Given information: The table shows the number of people who entered a store and the

total sales each hour.

Number of people	42	17	26	50	57	42	39	44	64	31
Total sales	155	33	109	240	237	129	136	189	271	105

Calculation:

The r value means “correlation coefficient” of the regression modal this number will tell, if correlation is positive or negative and how closely the equation is modeling the data. The closer the correlation coefficient is to 1 or -1, the more closely the equation models the data.

To use the graphing calculator the “correlation coefficient” of the regression modal on the above data is 0.96153463534215.

So r = 0.96153463534215.

c.

To determine

To find: a median −fit line for the data using graphical calculator.

Answer to Problem 4.6STP

The equation for median −fit line for the data is $y=5.03x-46.95$ .

Explanation of Solution

Given information: The table shows the number of people who entered a store and the

total sales each hour.

Number of people	42	17	26	50	57	42	39	44	64	31
Total sales	155	33	109	240	237	129	136	189	271	105

Formula used:

The equation for the linear regression modal 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:

Using the graphing calculator the equation for the linear regression modal on above table data is:

  $\begin{array}{l}\text{Sum}\text{of}x=412.\\ \text{Sum}\text{}\text{of}y=1604.\\ \text{Mean}x=\mathrm{41.2.}\\ \text{Mean}y=\mathrm{160.4.}\\ \text{Sum}\text{of}\text{squares}(S{S}_x)=\mathrm{1781.6.}\\ \text{Sum}\text{of}\text{products}(SP)=\mathrm{8966.2.}\\ \text{Linear}\text{equation}y=ax+b.\\ a=SP/S{S}_x=8966.2/1781.6=\mathrm{5.03267.}\\ b=M_y-a{M}_x=160.4-(5.03\times 41.2)=-\mathrm{46.94589.}\\ y=5.03267x-\mathrm{46.94589.}\end{array}$

So, the equation for median −fit line for the data is $y=5.03x-46.95$ .