Plotting a number of regression lines in a single plot - r

Question

How do I show 2 regression lines on the same plot?
Here are both models:
data(mtcars)
a <- lm(mpg~wt+hp)
b <- lm(mpg~wt+hp+wt*hp)
I plot wt on the x-axis, mpg on the y-axis and hp as the colour.
Here it is in base R:
cr <- colorRamp(c("yellow", "red"))
with(mtcars, {
plot(wt, mpg, col = rgb(cr(hp / max(hp)), max=255),
xlab="Weight", ylab="Miles per Gallon", pch=20)
})
Also, please show how to accomplish this in ggplot2.
Here's the plot:
library(ggplot2)
p <- ggplot(mtcars, aes(x = wt, y = mpg)) + geom_point(aes(col = hp))
p + scale_colour_gradientn(colours=c("green","black"))
Thanks in advance!

Answer 1

The documentation for geom_smooth practically tells you how to do this.
One can use the regression models to predict new values for y and then plot these on the same graph using geom_smooth().
Below is code for ggplot2 that produces what I think you want. The two lines overlap so much that it looks like only one line is plotted and I've set one linetype to dashed to demonstrate this.
I don't know how to achieve this in base R though.
data(mtcars)
library(ggplot2)
a <- lm(mpg~wt+hp, data = mtcars)
b <- lm(mpg~wt+hp+wt*hp, data = mtcars)
mtcars$pred.a <- predict(a)
mtcars$pred.b <- predict(b)
p <- ggplot(mtcars, aes(x = wt, y = mpg)) + geom_point(aes(col = hp)) +
scale_colour_gradientn(colours=c("green","black")) +
geom_smooth(aes(x = wt, y = pred.a), method = "lm", colour = "black", fill = NA) +
geom_smooth(aes(x = wt, y = pred.b), method = "lm", colour = "red", fill = NA, linetype = 4)
p

Answer 2

A base R solution:
a <- lm(mpg~wt+hp, data=mtcars)
b <- lm(mpg~wt+hp+wt*hp, data=mtcars)
wt <- mtcars[, "wt"]
idx <- sort(wt, index.return=TRUE)$ix
plot(mpg~wt, data=mtcars)
lines(wt[idx], predict(a)[idx], col="red")
lines(wt[idx], predict(b)[idx], col="blue")
However, it is not the best visualisation conceivable.

Answer 3

You are asking how to add a regression line, but your regression models produce a regression plane and a regression surface, both higher dimensional than a line. You can find a regression line by conditioning on a chosen value of hp, or show multiple lines for different values of hp.
Using base graphics you can use the Predict.Plot function in the TeachingDemos package to add prediction lines/curves to a plot for a fitted model (or 2). The interactive TkPredict' function in the same package will let you interact with the plot to choose conditioning values, then will produce the call toPredict.Plot` to create the current line. You can the combine the generated commands to include them on the same plot.