Chapter 4.4, Problem 9PPS

a.

To determine

The equation for the line of fit in slope-intercept form using the points $\left(3,73000\right)\text{ and }\left(6,67650\right)$ .

Answer to Problem 9PPS

The equation in slope-intercept form is $y=-\frac{5350}{3}x+78350$ .

Explanation of Solution

Given: The given scatter-plot data is shown as,

  

Calculation: The slope for the line of fit using the points $\left(3,73000\right)\text{ and }\left(6,67650\right)$ is evaluated as,

  $\begin{array}{c}m=\frac{67650-73000}{6-3}\mathrm{......}\left(\begin{array}{c}\left(x_1,y_1\right)\to \left(3,73000\right)\\ \left(x_2,y_2\right)\to \left(6,67650\right)\end{array}\right)\\ =-\frac{5350}{3}\end{array}$

Now, the equation for the line of fit is evaluated as,

  $\begin{array}{c}y-73000=-\frac{5350}{3}\left(x-3\right)\mathrm{......}\left(\begin{array}{l}\text{Here }m=-\frac{5350}{3}\text{ and}\\ \left(x_1,y_1\right)\to \left(3,73000\right)\end{array}\right)\\ y-73000=-\frac{5350}{3}x+5350\\ y=-\frac{5350}{3}x+78350\end{array}$

b.

To determine

The average attendance for the game in year 2012.

Answer to Problem 9PPS

The average attendance for the year 2012 is 56950.

Explanation of Solution

Given: The given scatter-plot data is shown as,

  

Calculation: The equation for the line of fit is $y=-\frac{5350}{3}x+78350$ . Now plugging for $x=12$ in this equation, because the base year is 2000.

  $\begin{array}{c}y=-\frac{5350}{3}\left(12\right)+78350\\ =56950\end{array}$

c.

To determine

Can you use equation for line of fit to make a decision about the average attendance in any given year in the future? Explain it.

Answer to Problem 9PPS

No, we cannot use the equation of line of fit to predict any kind of future attendance at game.

Explanation of Solution

Given: The given scatter-plot data is shown as,

  

Calculation: Since, we cannot use the equation of line of fit to estimate anything about future attendance because the average attendance can fluctuate with other variables. So it is not possible to predict in advance any decision about the average attendance in any given year in future.