How to compute the residuals of a linear model
Description
If a model has been fit to a dataset, the residuals are the differences between the actual data points and the results the model would predict. Given a linear model and a dataset, how can we compute those residuals?
Using statsmodels, in Python
Let’s assume that you’ve already built a linear model similar to the one below. This one uses a small amount of fake data, but it’s just an example.
1
2
3
4
5
6
7
import statsmodels.api as sm
xs = [ 393, 453, 553, 679, 729, 748, 817 ]
ys = [ 24, 25, 27, 36, 55, 68, 84 ]
xs = sm.add_constant( xs )
reg = sm.OLS( ys, xs ).fit()
We can extract the residuals of the model by calling the model’s resid attribute.
1
reg.resid
1
2
array([ 9.16263041, 2.19945659, -9.07249979, -16.79516483,
-4.43114302, 6.04718527, 12.88953537])
The result is an array of the residuals for every value in the data set.
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.
Solution, in R
Let’s assume that you’ve already built a linear model similar to the one below. This one uses a small amount of fake data, but it’s just an example. See also how to fit a linear model to two columns of data.
1
2
3
xs <- c( 393, 453, 553, 679, 729, 748, 817 )
ys <- c( 24, 25, 27, 36, 55, 68, 84 )
model <- lm(ys ~ xs)
We can extract the residuals of the model in either of two ways.
R has a built-in residuals() function for this purpose.
1
residuals(model)
1
2
1 2 3 4 5 6 7
9.162630 2.199457 -9.072500 -16.795165 -4.431143 6.047185 12.889535
The model itself has a $residuals attribute.
1
model$residuals
1
2
1 2 3 4 5 6 7
9.162630 2.199457 -9.072500 -16.795165 -4.431143 6.047185 12.889535
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.
Topics that include this task
Opportunities
This website does not yet contain a solution for this task in any of the following software packages.
- Excel
- Julia
If you can contribute a solution using any of these pieces of software, see our Contributing page for how to help extend this website.