Need help to locate my mistake
This is certainly ***NOT*** correct. (If you really got those numbers from Matlab, then Matlab is up to Puttee.)
It was my mistake =) I had calculated the straight line so the edge of the plot was the y-axis =)
Have you plotted your data?
(1) Fitting a straight line is ridiculous.
Yes, I guess we have to realise that in the project, and explain why it is not good enough =) Next step is to use exponential smoothing =)
(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.
It was clearly a bad mistake of mine! =(
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
Thanks =)
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.
This is great stuff!