Residuals and Residual Plots
Most likely a linear regression will not fit the data perfectly.
distance
The residual (e) for each data point is the ________________________
from the data point to the regression line. It is the error in __________________.
prediction
observed y value
To find the residual (e) of a data point, take the ________________________
predicted yˆ value
and subtract the __________________________
(y value from the linear regression). ( e  y  yˆ )
zero That is, Σ e =
The sum of the residuals is equal to _____.
Residual Plot
Residuals can be plotted on a scatterplot called a ____________________________.
x value
residual
The vertical y-axis is now the ________________________.
 The horizontal x-axis is the same ________________________ as the original graph.

LOOKING AT RESIDUAL PLOTS:
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,
shape
will have a _____________.
HOW TO USE RESIDUAL PLOTS:
If the residual plot is RANDOM: Use Linear Regression
If the residual plot is NON-random: DO NOT USE Linear Regression
Consider some other type of regression.
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.
How does the linear
regression fit the data?
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?
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.
How does the linear
regression fit the data?
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?
Non-Linear Data
A scatterplot and linear
regression line
are already drawn
from the given data.
Use a calculator to find the
linear regression for this data.
LinReg
y=ax+b
a=
Enter x-values into L1.
Enter y-values into L2.
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).
How does the linear
regression fit the data?
Complete the table.
Create a residual plot (right).
What do you notice about the
residual plot?