Fit a model with four predictors. All are linear. Notice the residuals versus fitted plot. Not great.

data(mtcars)
m <- lm(mpg ~ wt + disp + drat + qsec, data = mtcars)
plot(m, which = 1)

Use term plots to investigate departures from linearity for each coefficient. Notice how the smooth trend line for the predictor wt bends around the slope. This suggests a quadratic term may be more suitable.

op <- par(mfrow=c(2,2))
termplot(m, partial.resid=TRUE, smooth=panel.smooth)

par(op)

Add quadratic term for wt predictor. Now the fitted versus residuals plot looks better.

m2 <- lm(mpg ~ poly(wt,2) + disp + drat + qsec, data = mtcars)
plot(m2, which = 1)

The term plots also look better.

op <- par(mfrow=c(2,2))
termplot(m2, partial.resid=TRUE, smooth=panel.smooth)

par(op)

The car package also makes these plots using the crPlots() function.

library(car)
crPlots(m)