Exercise 1 Page 193

Let's begin by making a table of the residual values. Note that, in our table, $x$ represents the years since $2005$ and $y$ represents the attendance at the amusement park (in thousands).

$x$	$y$	$y = - 9.8 x + 850$	$y -$ value From Model	Residual
$0$	$850$	$- 9.8 (0) + 850$	$850$	$850 - 850 = 0$
$1$	$845$	$- 9.8 (1) + 850$	$840.2$	$845 - 840.2 = 4.8$
$2$	$828$	$- 9.8 (2) + 850$	$830.4$	$828 - 830.4 = - 2.4$
$3$	$798$	$- 9.8 (3) + 850$	$820.6$	$798 - 820.6 = - 22.6$
$4$	$800$	$- 9.8 (4) + 850$	$810.8$	$800 - 810.8 = - 10.8$
$5$	$792$	$- 9.8 (5) + 850$	$801$	$792 - 801 = - 9$
$6$	$785$	$- 9.8 (6) + 850$	$791.2$	$785 - 791.2 = - 6.2$
$7$	$781$	$- 9.8 (7) + 850$	$781.4$	$781 - 781.4 = - 0.4$
$8$	$775$	$- 9.8 (8) + 850$	$771.6$	$775 - 771.6 = 3.4$
$9$	$760$	$- 9.8 (9) + 850$	$761.8$	$760 - 761.8 = - 1.8$

Now we need to create a scatter plot using the given $x -$ values and our residuals. Recall that if the model is a good fit for the data, the scatter plot will be evenly distributed above and below the $x -$ axis. Also, there will be no apparent patterns.

Scatter plot of the points (0,0), (1,4.8), (2,-2.4), (3,-22.6), (4,-10.8), (5,-9), (6,-6.2), (7,-0.4), (8,3.4), (9,-1.8)

We can see that this line of fit does not model the data well. It is not evenly distributed above and below the $x -$ axis. The residual scatter plot shows that only two points are positive residuals, one point is perfectly explained by the line, and the rest are negative residuals.