In article <oJ6G5.700$[EMAIL PROTECTED]>,
Jennifer Howser <[EMAIL PROTECTED]> wrote:
>My text book states that the tandard error of the regression coefficient B^
>varies inversely with the variance of X, one can improve the significnance
>of the estimated parameter by selecting values of X at the endpoints of the
>range of possible values. However, it does not explain why it is desirable,
>could someone explain to me why.
One can see it most easily by looking at the what
happens if one only uses two X values. In that
case, the regression line is the usual line through
the points with those X values and the averages of
the Y values, or the slope is the difference of the
Y averages divided by the difference of the X values.
The variance of the difference of the Y averages is
the same, no matter what the X values are, so the
standard error of the regression coefficient varies
inversely with the difference of the X values. More
generally, it varies inversely with the standard
deviation (not variance) of X.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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