Algebra 2
Residuals and Residual Plot Notes
Today I will…
I’ll know I’ve got it when…
Essential Question…
Perfectly Linear Data
1. Draw a scatter plot of the data.
x
y
0
1
1
3
2
5
3
7
4
9
5
11
2. Find the linear regression for this data.
3. Draw the linear regression on the same graph as the scatter plot.
4. How does the linear regression fit the data?
5. Complete the residual table:
x
Observed Predicted Residual(e)
y
ŷ
e  y  yˆ
0
1
1
3
2
5
3
7
4
9
5
11
Sum of the residuals
7. What do you notice about the residual plot?
6. Make a residual plot:
Linear Data
1. Draw a scatter plot of the data:
x
y
0
2
1
5
2
4
3
4
4
8
5
10
2. Find the linear regression for this data.
3. Draw the linear regression on the same graph as the scatter plot.
4. How does the linear regression fit the data?
5. Complete the residual table:
x
Observed
y
0
2
1
5
2
4
3
4
4
8
5
10
Predicted
ŷ
6. Make a residual plot:
Residual(e)
e  y  yˆ
Sum of the residuals
7. What do you notice about the residual plot?
Non Linear Data
1. Draw a scatter plot of the data.
x
y
-2
.25
-1
.5
0
1
1
2
2
4
3
8
2. Does the data appear to be linear? If not, what kind of function would best fit this data?
3. Find the linear regression for this data.
4. Draw the linear regression on the same graph as the scatter plot.
5. How does the linear regression fit the data?
6. Complete the residual table:
x
Observed
y
-2
.25
-1
.5
0
1
1
2
2
4
3
8
Predicted
ŷ
7. Make a residual plot:
Residual(e)
e  y  yˆ
Sum of the residuals
8. What do you notice about this residual plot?
9. Summarize your observations about residual plots.
Teacher Notes
S. ID.6b Informally assess the fit of a function by plotting and analyzing residuals. *(Modeling Standard)
A video explaining Residuals and Residual plot is available at this site:
http://stattrek.com/regression/residual-analysis.aspx
In univariate numerical data analysis students use Mean as the measure to represent the data and make
predictions. In bivariate numerical data analysis, students will use a linear regression to represent a set of data
that appears to have a linear association.
Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the vertical
distance from the data point to the regression line. It is the error in prediction that the linear regression will
have for that data point. To find the residual (e) of a data point, take the observed y value and subtract the
predicted ŷ value (y value from the linear regression). ( e  y  yˆ )
Residuals can be plotted on a scatter plot. The x axis is the same independent variable as the original graph but
the y axis is now the residual axis.
When a set of data has a linear pattern, its residual plot will have a random pattern. If a set of data does not
have a linear pattern, its residual plot will not be random, but rather, will have a shape.
To evaluate whether or not a linear regression is appropriate for a set of data, have students look at the residual
plot. If the residual plot has a random pattern, a linear regression is appropriate. If a residual plot has a nonrandom pattern, consider another type of regression.