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# How do I compute the standard error (s.e.) of ''beta'' in a linear regression in SPSS?

Two estimates of covariate 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 may be used to obtain z-scores.

Alternatively (see for example Cohen and Cohen, 1983, p.100), you can compute standard errors using the standard deviations (s.ds) of the response and covariates.

$$\mbox{s.e.(beta) of a covariate = s.e.(B) of covariate} \frac{\mbox{s.d.(covariate)}}{\mbox{s.d.(response)}}$$

Jones and Waller (2013) give an overview of methods for computing confidence intervals for beta including the standard method of Cohen, Cohen, West and Aiken (2003 ,p.86) which they say is not always accurate and present R code for a suggested improved measure, the delta method.

References

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

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Erlbaum

Jones J. A. and Waller N. G. (2013) Computing confidence intervals for standardized regression coefficients. Psychological Methods 18(4), 435-453. R code is given in the appendix to produce the suggested (delta method) standard error for beta using simulated data which is also generated by the R code in the program.