Need help to locate my mistake

Dear readers

I would like to make General Linear Model (GLM) for the following  
data set
http://louise.hoffman.googlepages.com/fuel.csv

The code I have written is

fuelData<-read.table('fuel.csv',header=TRUE, sep=',')
n<-dim(fuelData)[1]
xOnes<- matrix(1,nrow=n,ncol=1)
x<-cbind(xOnes,fuelData[,3])
y<-fuelData[,4]
theta<-((t(x)%*%x)^(-1))%*%t(x)%*%y

which gives

theta

            [,1]
[1,] 215.8374077
[2,]   0.1083491

When I do it in Matlab I get theta to be
79.69
0.18

which is correct. ~79 is the crossing of the y-axis.

This is certainly ***NOT*** correct. (If you really got those numbers
from Matlab, then Matlab is up to Puttee.)

Have you plotted your data?

	(1) Fitting a straight line is ridiculous.

	(2) If you are so foolish as to fit a straight line, you get
	theta to have entries -4197.96 (intercept) and 2.16 (slope).
	The line y = 79.69 + 0.18*x is off the edge of the graph and
	does not even appear.

Have I perhaps written theta wrong?

Yes.  The expression (t(x)%*%x)^(-1) is the matrix of entry
	by entry reciprocals of the entries of t(x)%*%x.

	You want:

		theta <- solve(t(x)%*%x))%*%t(x)%*%y


	Anyhow, if you're going to use R, why not ***use R***?

	fit <- lm(fpi ~ rtime,data=fuelData)
	theta <- coef(fit)

	This gives an answer identical to that from the corrected version of
	your ``from scratch'' expression.  (That expression, while  
theoretically
	correct, is numerically ill-advised.  The cognoscenti use either the
	Choleski or the ``qr'' decomposition of t(x)%*%x to effect the  
calculations.
	One of these is what is going on in the bowels of lm().  But here I  
speak
	of that of which I know little.)

		cheers,

			Rolf Turner



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