Jennifer Howser 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.
Jenny:
Why it works: for roughly the same reason that of you wanted to nail a
6' plank to the wall with only four nails, it would be best to put them
near the ends of the plank. "Better leverage."
Why it's desirable: because you're estimating your parameter with less
error. Less error is good.
Why it's risky: by not making any observations near the middle of the
range you have _assumed_ that the linear model holds. If it doesn't you
have no way to check.
[A mark of bad research is the attitude: "This model is easy to
compute (or, worse, 'likely to give me publishable answers') so I shall
assume it" - often compared with the drunk in the joke who looked for
his car keys on the next street over from the one where he'd dropped
them because the street lights were brighter there!]
What to do about it: consider making a majority of observations at the
ends and the rest distributed through the interval; or a large majority
at the ends and the rest clustered in the middle.
-Robert Dawson
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