Don't have a clue!

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Don't have a clue!
Message posted by Judy Davis on November 9, 2000 at 12:00 AM (ET)

Yi = B + Ei
Show that the least-squares estimator of B in a model with solely a constant term as a regressor is the sample mean of the dependent variable.

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Re: Don't have a clue!
Message posted by Darius on November 9, 2000 at 12:00 AM (ET)

If Y(i)= B + E(i)
Its not regression, but one variable's statistics.
then B = the average of Y
the standard deviation (biased "n-1") is the usual one's
yp = B
n = the sample size

s= sqrt([Sum{(yi-yp)^2}]/[n-1])
or
s= sqrt([n*Sum{yi^2}-Sum{yi}^2]/[n*(n-1)])

Re: Don't have a clue!
Message posted by JG on November 9, 2000 at 12:00 AM (ET)

When E=0, then B is the least square
estimator of the mean of Y. You have to use calculus to do this or get the formulas from an introductory book of statistics and set E=0.

Re: Don't have a clue!
Message posted by Jack Tomsky on November 9, 2000 at 12:00 AM (ET)

Algebraically, the least-squares estimate of B, from the general linear model, with x(i) = 1 is,

B(est) = Sum[x(i)*y(i)]/Sum[x(i)] = Sum[y(i)]/N = ybar.

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