Name________________________________________ Per # _____
NOTES/Practice
Math 8 ACC
Date _____________
Interpreting Residual Plots
The sum of the residuals provides an idea of the
degree of accuracy when using the least-squares line to make predictions.
The following guidelines apply only if you have established this is a “causal” correlation.
 The closer the sum is to zero the more reliable the prediction MAY be.
 The greater the sum of the residuals the less reliable the predictions MAY be.
Graph I: Original Scatter plot
 The x-values are the inputs from

the original scatter plot data.
The y-values are the outputs from
the original scatter plot data.
Graph II: Residual Plot (same data)
 The x-values are the inputs from the

original scatter plot data.
The y-values are the RESIDUALS
found by calculating the differences
between the original outputs and
predicted outputs.
Characteristics of a residual plot that implies there is a linear relationship are:
There are no odd patterns or curved trends in the plot. It actually looks a bit scattered.
The irony is that even though a scattered appearance implied no correlation in a scatter
plot, a scattered appearance in a residual plot means “there is” a linear relationship.
 The sum of the residuals is zero
 The points are equally represented above and below the x-axis.

Be Careful!!!!
Sometimes, a scatter plot can look linear, but it really is not. Notice that the output (y-values)
scales are in increments of 25. Because, of the large scale value, it is hard to see the deviations
in the line.
When the residual differences are plotted, the appearance that would imply a linear connection is
not present. We will learn in upcoming lessons, what type of relationship this really is.
Constructing Residual Plots
EXAMPLE: Recall , from the previous residual notes, that we made linear regression of
y = x + 9 for the following data.
x
y
Actual
y
Predicted
Residual
10
20
19
+1
15
19
24
-5
18
30
27
+3
20
29
29
0
25
31
34
-3
25
35
34
1
Sum of the Residuals→
-3
In the previous example we questioned if the -3 implied a good linear fit or not (What is
close enough to zero and what is not?)The residual plots would imply that there, in fact, is
a linear relationship, since the residual show no obvious pattern.
Even if the linear function we created is adequate, one should investigate to see if there is
one that is more accurate.
Practice: Construct a residual plot based on the date below.
Line of Best Fit: y = 0.5x
y
y
original
predicted
5
3
2.5
0.5
10
4
5
-1
15
9
7.5
1.5
20
7
10
-3
25
13
12.5
0.5
x
RESIDUALS
Does it imply that the data is linear or nonlinear? _________________________
Explain your answer.