Let's begin by making a table of the residual values. Note that, in our table, y represents the approximate number (in thousands) of movie tickets sold in month x.
x
y
y=1.3x+27
y-value From Model
Residual
1
27
1.3( 1)+27
28.3
27-28.3= -1.3
2
28
1.3( 2)+27
29.6
28-29.6= -1.6
3
36
1.3( 3)+27
30.9
36-30.9= 5.1
4
28
1.3( 4)+27
32.2
28-32.2= -4.2
5
32
1.3( 5)+27
33.5
32-33.5= -1.5
6
35
1.3( 6)+27
34.8
35-34.8= 0.2
Now we can create a scatter plot using the given x-values and our residuals. Remember, 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.
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 two points are positive residuals and the rest are negative residuals.
