Linear regression dialog

This is a simple interface for studying power and sample-
size problems for simple or multiple linear regression
models.  It is designed to study the power of testing one
predictor, x[j], in the presence of other predictors.
The power of the t test of a regression coefficient
depends on the error SD, the SD of the predictor itself,
and the multiple correlation between that predictor and
other predictors in the model.  The latter is related to
the variance inflation factor.  It is assumed that the
intercept is included in the model.

The components in the dialog are as follows:

No. of predictors: Enter the total number of predictors
(independent variables) in the regression model.

SD of x[j]: Enter the standard deviation of the values of
the predictor of interest. This should be the so-called
'population' SD (sqrt{sum (x_ij - xbar_j)^2 / n}).

VIF[j]: (This slider appears only when there is more than
one predictor.)  Enter the variance-inflation factor for
x[j].  In an experiment where you can actually control
the x values, you probably should use an orthogonal
design where all of the predictors are mutually
uncorrelated -- in which case all the VIFs are 1.
Otherwise, you need some kind of pilot data to understand
how the predictors are correlated, and you can estimate
the VIFs from an analysis of those data.

Alpha: The desired significance level of the test.

Two-tailed: Check or uncheck this box depending on
whether you plan to use a two-tailed or a one-tailed
test.  If it is one-tailed, it is assumed right-tailed.
If a left-tailed test is to be studied, reverse the signs
and think in terms of a right-tailed test.

Error SD: The SD of the errors from the regression model.
You likely need pilot data or some experience using the
same measurement instrument.

Detectable beta[j]: The clinically meaningful value of
the regression coefficient that you want to be able to
detect.

Sample size: The total number of observations in the
regression dataset.  This is forced to be at least 2
greater than the number of predictors.

Power: The power of the t test, at the current settings
of thre parameter values.

Solve for: Determines what parameter is solved for when
you change the value of the Power slider.
