1. distance prediction observed y value predicted value zero
Residuals and Residual Plots
Most likely a linear regression will not fit the data perfectly.
The residual (e) for each data point is the ________________________
from the data point to the regression line. It is the error in __________________.
To find the residual (e) of a data point, take the ________________________
and subtract the __________________________ (y value from the linear regression).
The sum of the residuals is equal to _____. That is, Σ e =
Residuals can be plotted on a scatterplot called a ____________________________.
The horizontal x-axis is the same ________________________ as the original graph.
The vertical y-axis is now the ________________________.
LOOKING AT RESIDUAL PLOTS:
When a set of data has a linear pattern, its
residual plot will have a ____________________________.
If a set of data does not have a linear pattern, its
residual plot will _______________________, but rather,
will have a _____________.
HOW TO USE RESIDUAL PLOTS:
If the residual plot is RANDOM:
If the residual plot is NON-random:
distance
prediction
observed y value
predicted value
zero
Residual Plot
x value
residual
random pattern
NOT be random
shape
Use Linear Regression
DO NOT USE Linear Regression
Consider some other type of regression.

2. Perfectly Linear Data
Draw a scatterplot
from the given data.
Enter x-values into L1.
Enter y-values into L2.
Use a calculator to find the
linear regression for this data.
LinReg
y=ax+b a= b=
r2= r=
Linear regression equation:
Draw the linear regression on the same graph as the scatter plot (left).
Enter linear regression into Y1.
Use the table feature on the calculator to fill in the center column on the residual table (top right).
Complete the table.
Create a residual plot (right).
What do you notice about the residual plot?
How does the linear regression fit the data?

3. Linear Data A scatterplot and linear regression line
are already drawn
from the given data.
Enter x-values into L1.
Enter y-values into L2.
Use a calculator to find the
linear regression for this data.
LinReg
y=ax+b a= b=
r2= r=
Linear regression equation:
Enter linear regression into Y1.
Use the table feature on the calculator to fill in the center column on the residual table (top right).
Complete the table.
Create a residual plot (right).
What do you notice about the residual plot?
How does the linear regression fit the data?

4. Non-Linear Data
A scatterplot and linear
regression line
are already drawn
from the given data.
Enter x-values into L1.
Enter y-values into L2.
Use a calculator to find the
linear regression for this data.
LinReg
y=ax+b a= b=
r2= r=
Linear regression equation:
Enter linear regression into Y1.
Use the table feature on the calculator to fill in the center column on the residual table (top right).
Complete the table.
Create a residual plot (right).
What do you notice about the residual plot?
How does the linear regression fit the data?