Chapter 8.9, Problem 3PPS

(a)

To determine

Sketch a scatter plot for the baseball and softball with the line of fit.

Year	Equipment sales ($ millions)
Baseball and softball	Tennis
$2001$	$277$	$296$
$2002$	$290$	$319$
$2003$	$304$	$318$
$2004$	$329$	$338$
$2005$	$319$	$383$
$2006$	$316$	$371$
$2007$	$334$	$358$
$2008$	$340$	$343$
$2009$	$346$	$362$
$2010$	$356$	$373$

Answer to Problem 3PPS

The scatter plot and the line of fits are shown by the following graph:

  

Explanation of Solution

Given:

Year	Equipment sales ($ millions)
Baseball and softball	Tennis
$2001$	$277$	$296$
$2002$	$290$	$319$
$2003$	$304$	$318$
$2004$	$329$	$338$
$2005$	$319$	$383$
$2006$	$316$	$371$
$2007$	$334$	$358$
$2008$	$340$	$343$
$2009$	$346$	$362$
$2010$	$356$	$373$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

Consider,

Year: $x$

Baseball and softball: $y$

There are ten points are given as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(2001,277\right)\\ B=\left(x_2,y_2\right)=\left(2002,290\right)\\ C=\left(x_3,y_3\right)=\left(2003,304\right)\\ D=\left(x_4,y_4\right)=\left(2004,329\right)\\ E=\left(x_5,y_5\right)=\left(2005,319\right)\\ F=\left(x_6,y_6\right)=\left(2006,316\right)\\ G=\left(x_7,y_7\right)=\left(2007,334\right)\\ H=\left(x_8,y_8\right)=\left(2008,340\right)\\ I=\left(x_9,y_9\right)=\left(2009,346\right)\\ J=\left(x_{10},y_{10}\right)=\left(2010,356\right)\end{array}$

Now use any two points to calculate the slope intercept from equation:

  $m=\frac{y_3-y_1}{x_3-x_1}=\frac{304-277}{2003-2001}=\frac{27}{2}$

Now, the slope intercept form equation is written as:

  $\begin{array}{l}y=mx+b\\ y=\frac{27}{2}x+b\end{array}$

Now put the value of $\left(x_1,y_1\right)=\left(2001,277\right)$ in the above eq. to get the Y-intercept:

  $\begin{array}{l}y=mx+b\\ 277=\frac{27}{2}\left(2001\right)+b\\ b=277-27013.5\\ b=-26736.5\end{array}$

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=\frac{27}{2}x-26736.5\end{array}$

The scatter plot and the line of fits are shown by the following graph by using the above data points and line of fit eq. or slope-intercept form eq.

  

Conclusion:

Hence, with the help of slope-intercept form the line of fit is drawn as above.

(b)

To determine

The number of sales of in $2015$ with the line of fit equation from the first subpart

Answer to Problem 3PPS

The sales of football and soft ball for $2015$ is $466$

Explanation of Solution

Given:

  $x=2015$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

From the first subpart:

The final slope intercept form equation is derived as:

  $\begin{array}{l}y=mx+b\\ y=\frac{27}{2}x-26736.5\end{array}$

Now, to calculate the number of sales softball and basketball $y$ , need to put $x=2015$ in above eq.

  $\begin{array}{l}y=mx+b\\ y=\frac{27}{2}x-26736.5\\ y=\frac{27}{2}\left(2015\right)-26736.5\\ y=27202.5-26736.5\\ y=466\end{array}$

Conclusion:

Hence, sales of baseball and softball ball for $2015$ are calculated as $y=466$ by using the line fit.

(c)

To determine

Sketch a scatter plot for the tennis sales with the line of fit.

Year	Equipment sales ($ millions)
Baseball and softball	Tennis
$2001$	$277$	$296$
$2002$	$290$	$319$
$2003$	$304$	$318$
$2004$	$329$	$338$
$2005$	$319$	$383$
$2006$	$316$	$371$
$2007$	$334$	$358$
$2008$	$340$	$343$
$2009$	$346$	$362$
$2010$	$356$	$373$

Answer to Problem 3PPS

The scatter plot and the line of fits are shown by the following graph:

  

Explanation of Solution

Given:

Year	Equipment sales ($ millions)
Baseball and softball	Tennis
$2001$	$277$	$296$
$2002$	$290$	$319$
$2003$	$304$	$318$
$2004$	$329$	$338$
$2005$	$319$	$383$
$2006$	$316$	$371$
$2007$	$334$	$358$
$2008$	$340$	$343$
$2009$	$346$	$362$
$2010$	$356$	$373$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

Consider,

Year: $x$

Tennis: $y$

There are ten points are given as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(2001,296\right)\\ B=\left(x_2,y_2\right)=\left(2002,319\right)\\ C=\left(x_3,y_3\right)=\left(2003,318\right)\\ D=\left(x_4,y_4\right)=\left(2004,338\right)\\ E=\left(x_5,y_5\right)=\left(2005,383\right)\\ F=\left(x_6,y_6\right)=\left(2006,371\right)\\ G=\left(x_7,y_7\right)=\left(2007,358\right)\\ H=\left(x_8,y_8\right)=\left(2008,343\right)\\ I=\left(x_9,y_9\right)=\left(2009,362\right)\\ J=\left(x_{10},y_{10}\right)=\left(2010,373\right)\end{array}$

Now use any two points to calculate the slope intercept from equation:

  $m=\frac{y_3-y_1}{x_3-x_1}=\frac{318-296}{2003-2001}=\frac{22}{2}=11$

Now, the slope intercept form equation is written as:

  $\begin{array}{l}y=mx+b\\ y=11x+b\end{array}$

Now put the value of $\left(x_1,y_1\right)=\left(2001,296\right)$ in the above eq. to get the Y-intercept:

  $\begin{array}{l}y=mx+b\\ 296=11\left(2001\right)+b\\ b=296-22011\\ b=-21715\end{array}$

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=11x-21715\end{array}$

The scatter plot and the line of fits are shown by the following graph by using the above data points and line of fit eq. or slope-intercept form eq.

  

Conclusion:

Hence, with the help of slope-intercept form the line of fit is drawn as above.

(d)

To determine

The number of sales of tennis in the year $2020$ with the line of fit equation from the first subpart

Answer to Problem 3PPS

The sales of tennis for $2020$ is $466$

Explanation of Solution

Given:

  $x=2020$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

From the first subpart:

The final slope intercept form equation is derived as:

  $\begin{array}{l}y=mx+b\\ y=11x-21715\end{array}$

Now, to calculate the number of Sunday newspapers $y$ , need to put $x=2020$ in above eq.

  $\begin{array}{l}y=mx+b\\ y=11x-21715\\ y=11\left(2020\right)-21715\\ y=22220-21715\\ y=505\end{array}$

Conclusion:

Hence, sales of tennis for $2020$ are calculated as $y=505$ by using the line fit.