hi,
i am reading on regression, and the presumptions it made were:
1. all the error terms Ei's have the same constant variance (sigma squared)
2. all of the Yi's have that same variance (sigma squared) but different
means that depend on the unknown constants Xi's
later it mentions that a common objective in a regression analysis is to
estimate the mean for one or more probability distributins of Y. so if Xh
denote the level of X we wish to estimate a mean response(Xh may be a valuse
that occured in a sample, ir some other value within the scope of the
model)E{Yh} is the mean response for that Xh.
if you plot the regression line with the confidence interval limits for each
Yh, youll see that if you were close to Xbar the confidence limits will be
closer than if you went to an Xh farther from Xbar.
that is because the variance for that Yh depends on the X....
my question is: i thought that all Y's have the same variance. i know that
this is predicted. is it differnet from the fitted Yhats that you get when
you insert a regression line? arent the variances of the fitted Ybars equal?
what is the differencem and why are the variances different in this case?
thank you for your help
.
.
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