Plot "regression line" from multiple regression in R

Question

I ran a multiple regression with several continuous predictors, a few of which came out significant, and I'd like to create a scatterplot or scatter-like plot of my DV against one of the predictors, including a "regression line". How can I do this?

My plot looks like this

D = my.data; plot( D$probCategorySame, D$posttestScore )

If it were simple regression, I could add a regression line like this:

lmSimple <- lm( posttestScore ~ probCategorySame, data=D )
abline( lmSimple ) 

But my actual model is like this:

lmMultiple <- lm( posttestScore ~ pretestScore + probCategorySame + probDataRelated + practiceAccuracy + practiceNumTrials, data=D )

I would like to add a regression line that reflects the coefficient and intercept from the actual model instead of the simplified one. I think I'd be happy to assume mean values for all other predictors in order to do this, although I'm ready to hear advice to the contrary.

This might make no difference, but I'll mention just in case, the situation is complicated slightly by the fact that I probably will not want to plot the original data. Instead, I'd like to plot mean values of the DV for binned values of the predictor, like so:

D[,'probCSBinned'] = cut( my.data$probCategorySame, as.numeric( seq( 0,1,0.04 ) ), include.lowest=TRUE, right=FALSE, labels=FALSE )
D = aggregate( posttestScore~probCSBinned, data=D, FUN=mean )
plot( D$probCSBinned, D$posttestScore )

Just because it happens to look much cleaner for my data when I do it this way.

Answer 1

To plot the individual terms in a linear or generalised linear model (ie, fit with lm or glm), use termplot. No need for binning or other manipulation.

# plot everything on one page
par(mfrow=c(2,3))
termplot(lmMultiple)

# plot individual term
par(mfrow=c(1,1))
termplot(lmMultiple, terms="preTestScore")

Answer 2

You need to create a vector of x-values in the domain of your plot and predict their corresponding y-values from your model. To do this, you need to inject this vector into a dataframe comprised of variables that match those in your model. You stated that you are OK with keeping the other variables fixed at their mean values, so I have used that approach in my solution. Whether or not the x-values you are predicting are actually legal given the other values in your plot should probably be something you consider when setting this up.

Without sample data I can't be sure this will work exactly for you, so I apologize if there are any bugs below, but this should at least illustrate the approach.

# Setup
xmin = 0; xmax=10 # domain of your plot
D = my.data
plot( D$probCategorySame, D$posttestScore, xlim=c(xmin,xmax) )
lmMultiple <- lm( posttestScore ~ pretestScore + probCategorySame + probDataRelated + practiceAccuracy + practiceNumTrials, data=D )

# create a dummy dataframe where all variables = their mean value for each record
# except the variable we want to plot, which will vary incrementally over the 
# domain of the plot. We need this object to get the predicted values we
# want to plot.
N=1e4
means = colMeans(D)
dummyDF = t(as.data.frame(means))
for(i in 2:N){dummyDF=rbind(dummyDF,means)} # There's probably a more elegant way to do this.
xv=seq(xmin,xmax, length.out=N)
dummyDF$probCSBinned = xv 
# if this gives you a warning about "Coercing LHS to list," use bracket syntax:
#dummyDF[,k] = xv # where k is the column index of the variable `posttestScore`

# Getting and plotting predictions over our dummy data.
yv=predict(lmMultiple, newdata=subset(dummyDF, select=c(-posttestScore)))
lines(xv, yv)

Answer 3

Look at the Predict.Plot function in the TeachingDemos package for one option to plot one predictor vs. the response at a given value of the other predictors.