# example where r^2 is close to 0,
# but there is a strong nonlinear fit

x1 <- seq(-1,1,.01)
y1 <- x1^2 + rnorm(length(x1),0,.02)
fit1 <- lm(y1 ~ x1)
summary(fit1)
plot(x1,fit1$residuals)

# example where r^2 is close to 1, but a linear fit
# is far inferior to a nonlinear fit.

x2 <- seq(0,1,.005)
y2 <- x2^2 + rnorm(length(x2),0,.005)
fit2 <- lm(y2~x2)
summary(fit2)
plot(x2,fit2$residuals)