3d plot of regression squared error
On Thursday 03 March 2005 13:04, Ross Clement wrote:
Hi. I'm trying to create a 3d plot for a teaching example of finding a least-squares estimate of the parameters to fit a line to some data. I was hoping to get a nice plot with a clear, single minima where the derivative of the surface is zero. No matter how much I tinker, I can't seem to get a simple straightforward plot. Am I doing something wrong? Thanks in anticipation, Ross-c x <- c( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ) y <- c( 3, 4.2, 8.7, 11.7, 13.2, 19.1, 21, 25, 26.1, 29.8 )
Well, you need to go far enough away to see the curve. Centering the x-variable is important (at least with your parametrization of straight lines). E.g., the following combination gives a surface that looks nice enough: x <- 1:10 - 5.5 a.axis <- seq( 0, 10, length=20 ) b.axis <- seq( -30, 0, length=20 ) -Deepayan
sqe <- function( a, b ) {
total <- 0
for ( i in 1:length(x) ) {
diff <- y[i] - a * x[i] + b
total <- total + diff * diff
}
return( total )
}
df <- data.frame( x=x, y=y )
lm( y ~ x, df )
a.axis <- seq( -5, 10, length=20 )
b.axis <- seq( -20, 20, length=30 )
z <- outer( a.axis, b.axis, sqe )
persp( a.axis, b.axis, z, col="light grey", xlab="a", ylab="b",
zlab="sum.squared.error", theta=45 )