Chapter 8.9, Problem 1CYU

(a)

To determine

Sketch a scatter plot with the line of fit.

Year	$2001$	$2002$	$2003$	$2004$	$2005$	$2006$	$2007$
Number of Sunday newspapers	$913$	$913$	$917$	$915$	$917$	$907$	$907$

Answer to Problem 1CYU

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

  

Explanation of Solution

Given:

Year	$2001$	$2002$	$2003$	$2004$	$2005$	$2006$	$2007$
Number of Sunday newspapers	$913$	$913$	$917$	$915$	$917$	$907$	$907$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

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

Calculation:

Consider,

Year: $x$

Number of Sunday newspapers: $y$

There are seven points are given as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(2001,913\right)\\ B=\left(x_2,y_2\right)=\left(2002,913\right)\\ C=\left(x_3,y_3\right)=\left(2003,917\right)\\ D=\left(x_4,y_4\right)=\left(2004,915\right)\\ E=\left(x_5,y_5\right)=\left(2005,917\right)\\ F=\left(x_6,y_6\right)=\left(2006,907\right)\\ G=\left(x_7,y_7\right)=\left(2007,907\right)\end{array}$

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

  $m=\frac{y_3-y_1}{x_3-x_1}=\frac{917-913}{2003-2001}=\frac{4}{2}=2$

Now, the slope intercept form equation is written as:

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

Now put the value of $\left(x_1,y_1\right)=\left(2001,913\right)$ in the above eq. to get the Y-intercept:

  $\begin{array}{l}y=mx+b\\ 913=2\left(2001\right)+b\\ b=913-4001\\ b=-3088\end{array}$

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=2x-3088\end{array}$

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 Sunday newspapers in $2004$ in the US with the line of fit equation

Answer to Problem 1CYU

There are $940$ Sunday newspapers for $2004$ in the US

Explanation of Solution

Given:

  $x=2004$

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:

  $\begin{array}{l}y=mx+b\\ y=2x-3088\end{array}$

Now, to calculate the number of Sunday newspapers $y$ , need to put $x=2004$ in above eq.

  $\begin{array}{l}y=mx+b\\ y=2\left(2014\right)-3088\\ y=4028-3088\\ y=940\end{array}$

Conclusion:

Hence, Sunday newspapers for $2004$ in the US are calculated as $y=940$ by using the line fit.