Question: Population Regression

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Question: Population Regression
Message posted by Chris Billings on December 17, 2000 at 12:00 AM (ET)

Hello:

I am having trouble with one concept and would like to request your assistance.

Regarding simple regression analysis, will a population reression line always yield the mean of the y's for a given indepent variable x? I am having difficulty understanding how this might be?

Thank you for your consideration,
Chris Billings

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Question: Population Regression
Message posted by Phil on December 18, 2000 at 12:00 AM (ET)

The regression line is a line that best "fits" the data based on minimizing the sum of squares. If you have a line that is a "good fit", then the predicted value of Y given X may be a very good "estimate" of the mean of Y for that value of X. I doubt it would be "exact" mean of Y at that point.

(Not sure if that helped you much).

Re: Question: Population Regression
Message posted by Darius on December 18, 2000 at 12:00 AM (ET)

"the reression line always yield the mean of the y's for a given indepent variable x"

If you mean that for every x you obtain the mean of the y's : the ecuation is Yi= A*xi+B so:
if A=0 then Y=B=Average(Y)
So there is no relation between variable X and variable Y.

If you mean that for a given x you obtain a y value that is the average of the points at the same x ( more or less) >> in the regression line it suppouse to be a normal distribution of the y values arround the line.

I hope it helps

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