Chapter SH, Problem 2.15EP

a.

To determine

To represent: a scatter plot, graph a line fit, and describe the correlation of the given condition.

Answer to Problem 2.15EP

“Strong Positive Correlation.”

Explanation of Solution

Given:

The table shows the number shows the LCD televisions sold in the recent year:

Year	Numbers of TVs sold
2006	$733$
2007	$838$
2008	$943$
2009	$1048$
2015	$?$

Calculation:

Consider the data that represents the number of LCD televisions sold in various years at an electronic store. Assume that x represents the number of years since 2000.

To draw a scatter plot in Excel, first select data to plot and go to “Insert” menu, then go to “charts” and click on “Scatter plot”. Label both axis and the scatter plot of the given data is as follows:

  

The points $\left(6,733\right)\text{ and}\left(9,1048\right)$ will represent the data well. Draw a line through these two points. The line of fir is as follows:

  

The given data shows a “Strong Positive Correlation.”

b.

To determine

To write: a prediction equation by using two ordered pairs.

Answer to Problem 2.15EP

  $y=105x+103$ .

Explanation of Solution

Given:

The given ordered pairs $\left(6,733\right)\text{ and}\left(9,1048\right)$

Calculation:

To find an equation of a line through. The slope of the line will be,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{1048-733}{9-6}\\ =\frac{315}{3}=105\end{array}$

The equation of the line will be,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-733=105\left(x-6\right)\\ y=105x-630+733\\ y=105x+103\end{array}$

Therefore, the equation of the line is $y=105x+103$ ,

c.

To determine

To predict: the missing value of the given table.

Answer to Problem 2.15EP

  $1678$ .

Explanation of Solution

Given:

The table shows the number shows the LCD televisions sold in the recent year:

Year	Numbers of TVs sold
2006	$733$
2007	$838$
2008	$943$
2009	$1048$
2015	$?$

Calculation:

To compute the number of LCDs sold in 2015, substitute $x=15$ in equation $y=105x+103$ ,

  $\begin{array}{l}y=105\times 15+103\\ y=1575+103\\ y=1678\end{array}$

Therefore, the predicted number of LCDs sold in 2015 is equal to $1678$