= How do I compute the standard error of beta in a linear regression in SPSS?=

Two estimates of regression coefficients are given in SPSS. These are called B and beta and correspond to using raw score (response and predictor variables) and z-scored response and predictor variables respectively.

The Descriptives procedure [:FAQ/zscore: may be used] to obtain z-scores.

Alternatively (see for example Cohen and Cohen, 1983), $$ \mbox{s.e.(beta) = s.e.(B)} \frac{\mbox{s.d.(covariate)}}{\mbox{s.d.(response)}}$$

Reference

Cohen J. and Cohen P. (1983) Applied multiple regression/correlation analysis for the behavioral sciences Second Edition. lawrence Erlbaum: Hillsdale, NJ.