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=-9.8x+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 and there will be no apparent patterns.
We can see that this line of fit does not model the data well because the data points are 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.
