Re: One-sided p-values in regression


cornelius1729 wrote:
I'd like to extend the concept of a one-sided p-value to linear
regression.

The basic model for a linear regression is y = a + b*x1 + c*x2 +...
where xi are explanatory variables; a, b,c, ... are coefficients to be
determined; and y is the response variable.

The p-values for each coefficient calculated from a regression are the
probabilities that the coefficient has been incorrectly judged to be
non-zero.

The one-sided equivalent would be p-values of the probability that the
coefficient has been incorrectly judged to be greater than (less than)
zero.

This seems to be meaningful, but I'm not sure how you would go about
calculating the values. Any suggestions?

If the estimated coefficient b > 0,
The p-value for Ha: b > 0 is 1/2 of the two sided p-value given.
The p-value for Ha: b < 0 is 1 - 1/2 of the two sided p-value
given.

If the estimated coefficient b < 0.
The p-value for Ha: b > 0 is 1 - 1/2 of the two sided p-value
given.
The p-value for Ha: b < 0 is 1/2 of the two sided p-value given.

Note that in cases 2 and 3, the p-values will be greater than 0.5.

p--value = Pr ( Test Statistic is MORE EXTREME (by Ha) than the
actually observed value of the test statistic).

The above 4 cases are based on the above definition. You should
be able to work our why.

-- Reef Fish Bob.

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