rss_3dplot.R

# Creates a 3D plot to demonstrate how a combination of OLS parameters minimizes residual sum of squares

# set values for X
x <- seq(-50, 50, 1)

# Y as a function of X with random error
y <- NA
for (i in 1:length(x)) {
	y[i] <- 2*x[i] + rnorm(1, 0, 5)
}

# combine x values in design matrix with a column of 1's for the intercept
X <- cbind(1, x)

# Define function for RSS
RSS <- function(beta0, beta1) {
	beta <- c(beta0, beta1)
	# define how to calculate e'e (RSS matrix)
	ee <- t(y - X %*% beta) %*% (y - X %*% beta)
	return(ee)
}

# sequences for "possible" values of the parameters
a <- seq(-200,200,10)
b <- seq(-4,8,0.5)
# get RSS for combinations of possible parameter values
rss <- outer(a, b, function(x,y) mapply(RSS, x, y))
# 3D plot of the contour
persp(x = a, y = b, z = rss,
	theta=120, phi=20,
	col="cyan", border="darkblue", shade=TRUE,
	ticktype="simple",
	xlim=c(-200,200),
	ylim=c(-4,8),
	ylab="α",
	xlab="β",
	zlab="RSS"
)