# Re: Standard error of mean predictions

*From*: Allen McIntosh <nospam@xxxxxxxxxxxxxxxx>*Date*: Wed, 31 Oct 2007 22:24:24 -0400

Ray Koopman wrote:

On Oct 31, 3:31 am, Pekka Jarvela <pekkajarv...@xxxxxxxxx> wrote:SPSS gives as one of the columns SEP_1 which is according to SPSS help

"S.E. of mean predictions. Standard errors of the predicted values. An

estimate of the standard deviation of the average value of the

dependent variable for cases that have the same values of the

independent variables."

But how is it calculated? I have found only formulas for simple

regression y = b0 + b1X case but not for multivariable case. Any links

or hints would be appreciated.

The standard error of the predicted value of y for a given vector x

of predictor scores can be expressed as the product of three terms:

s(yhat|x) = s(y) * sqrt[(1-R^2)(n-1)/(n-p-1)] *

sqrt[1/n + D(x)^2/(n-1)],

where s(y) = the s.d. of y, R = the multiple correlation, n = the

sample size, p = the number of predictors, and D(x) = the Mahalanobis

distance of x from the centroid of the predictor distribution.

You could also try the Wikipedia article on multiple linear regression. The explanation is terse, but the basic results are there.

.

**References**:**Re: Standard error of mean predictions***From:*Ray Koopman

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