tosik tosik - 23 days ago 6
R Question

Why fitted values do not lie on the fitted line

I have very basic question regarding understanding linear regression model. Consider simple case when $y = a + bx + e$, where $e$ is the error term. I use OLS to estimate coefficients $a$ and $b$. Then fitted values are $\hat y = \hat a + \hat b x$. Should not they lie on the same line, since it is linear relationship? I ask because I do simple manipulations in R and have counterintuitive results

x <- rnorm(20, 3, 1)
y <- 12 + 4*x + rnorm(20, 0, 0.5)
m <- lm(y ~ x)
a <- coef(m)[1]
b = coef(m)[2]
plot(x, y) #plot initial data
abline(a = a, b = b, lwd = 2, col = 2) #plot fitted line
points(x = m$fitted.values, col = 4, pch = 4) #plot fitted values
legend('topleft', c("Actual", "Fitted line", "Fitted values"), col = c(1, 2, 4), pch = c(1, 1, 4), lty = c(0, 1, 0))


enter image description here

Why fitted values do not lie on the fitted line?

Answer

Replace the last line with

points(x = x, y = m$fitted.values, col = 4, pch = 4) #plot fitted values

The fitted values are for $y$, not for $x$.