Predicted by residual plot in R

I'm wondering what the difference is between:

1. 'predicted by residual plot' where I plot the residuals of the regression with the predicted values of the regression ;
2. the case where I plot the residuals with the predictor variables.

Also I'm wondering how to make such a plot in R in the case of multiple regression. Do I have to make a plot for each predictor separately?

• Here is an web-based, interactive tool for plotting regression results in three dimensions. You can enter your data set through an online form at the bottom of the page. This 3-D plot works with one dependent variable and two explanatory variables. You can also set the intercept to zero (i.e., remove the intercept from the regression equation). The graphics require a WebGL-capable browser. The most recent versions of all major desktop browsers support WebGL (although Safari's WebGL might be disabled by default, a – Android 3D Jan 15 '14 at 21:15
• @Android3D Because you already posted this answer at stats.stackexchange.com/questions/73320/…, I am converting it to a comment here. – whuber Jan 15 '14 at 21:19

A plot of residuals versus predicted response is essentially used to spot possible heteroskedasticity (non-constant variance across the range of the predicted values), as well as influential observations (possible outliers). Usually, we expect such plot to exhibit no particular pattern (a funnel-like plot would indicate that variance increase with mean). Plotting residuals against one predictor can be used to check the linearity assumption. Again, we do not expect any systematic structure in this plot, which would otherwise suggest some transformation (of the response variable or the predictor) or the addition of higher-order (e.g., quadratic) terms in the initial model.

More information can be found in any textbook on regression or on-line, e.g. Graphical Residual Analysis or Using Plots to Check Model Assumptions.

As for the case where you have to deal with multiple predictors, you can use partial residual plot, available in R in the car (crPlot) or faraway (prplot) package. However, if you are willing to spend some time reading on-line documentation, I highly recommend installing the rms package and its ecosystem of goodies for regression modeling.

• and in the case of plotting the residuals with the predictors to check linearity that means that you plot the same residuals with the different predictoes. does it need to be linear with each predictor? – upabove Nov 11 '11 at 14:32
• No, when you have multiple predictors, you don't use the regular residuals but instead the partial residuals; this is known as either a component-plus-residual plot (crplot in car) or a partial residual plot (prplot in faraway); however, curvature from other predictors can "leak" into these plots, so they're not guaranteed to give you exactly what you want. A CERES plot (also in car) is better but still not perfect. These plots are indeed created for each predictor in the model separately, I believe car has a function to do them all at once and faraway may too. – Aaron Nov 11 '11 at 16:41
• Here's a function to make all the prplots for a given lm fit, using ggplot2: gist.github.com/3041812. – Quantitative Historian Jul 3 '12 at 22:18

After you fit an lm object, you can plot it.

e.g.:

model <- lm(y~x,data=data.frame(y=rnorm(25),x=rnorm(25)))
plot(model)
?plot.lm

edit: example 2, which you should have posted yourself:

rm(list = ls(all = TRUE)) #CLEAR WORKSPACE
library(foreign)