Re: linear regression results approximates to the mean of Y

On May 29, 3:06 am, feilian <bs...@xxxxxxx> wrote:
I do a linear regression on a data set {(Xi,Yi)| i=1,……n} and get a
linear function Y=AX;

You could use

(Y-mean(Y)) = A*(X-mean(X))

but it is better to use

Y = A*X + B

then, when using a test set , I find that the mean of estimated
results always near mean(Y).

If the test (out of sample) set is drawn from
the same probability distribution as the training
(in sample) set, this is what you would expect if
both sets are sufficiently large. After all, both
sample means are estimates of the population mean.

Does this mean the X and Y have no linear relations?

No, and I don't understand why you would think so.

I don't know  whether I expressed clearly?

Your confusion can be minimized, if
1. you always include an intercept term in your
model
2. You apply your model to data that is assumed
to come from the same distribution as the
training data used to estimate A and B.
3. Both sets are sufficiently lage

Hope this helps.

Greg


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