# Thread: How to interpret the standard error of regression coefficients

1. ## How to interpret the standard error of regression coefficients

Hi folks, This is my first post here - I have read all the rules - please forgive me if I break one!

I have run an ANCOVA in SPSS. Obviously, in the ANCOVA we have a treatment (fixed effect factor, e.g., Density) and a covariate (e.g., sflower or sgerminate) and we have run the interaction of the covariate and factor (because this is the part we are particularly interested in).

In the "Parameter Estimates" we find the covariate estimates and we have figured out that one level of the factor x covariate interaction will be considered the null (e.g., Density = Low x sgerminate), which means its estimate of the regression coefficient is the same as the regression coefficient of the covariate alone (I'm going to call that B). The remaining regression coefficients of the remaining factor levels x covariate appear as C and I am able then to interpret the regression coefficients of the remaining levels of the factor x covariate as B+C.

But how do I interpret the standard error of the regression coefficients for each of the levels of the factor x covariate? Do I simply add the SE of a given level of the factor x covariate to the SE of the covariate?

Thank you for reading this and considering my question.

2. ## Re: How to interpret the standard error of regression coefficients

I have not seen interaction treated that way either in regression or in ANOVA. I was curious where you found this approach to analyzing an interaction. You can generate simple effects for the main effects and test them through the standard error, but I have never seen anyone test a level of an interaction for significance (which is what you would essentially be doing by calculating the SE).

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