# Re: [R] Need help to locate my mistake

From: Rolf Turner <r.turner_at_auckland.ac.nz>
Date: Mon, 03 Mar 2008 09:55:56 +1300

On 3/03/2008, at 9:18 AM, Louise Hoffman wrote:

>
> I would like to make General Linear Model (GLM) for the following
> data set
>
> The code I have written is
>
> 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.)

(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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