A research project I am part of is using multiple demographic variables to predict performance on a continuous scale item measuring a specific behavior so that we can describe people of trait X+Y+Z are likely to have the greatest elevations on this scale. Included variables are both continuous and dummy coded binaries (for example, income is an included continuous variable and gender is a binary). The variables have been entered into the linear regression model in blocks consistent with theoretical realms of influence for the dependent variable (e.g., social factors, physical factors, etc). One of these factors is ethnicity which we have dummy coded for this analysis.
When we first ran the regression analysis, it excluded the first dummy coded variable from the output and it appeared to use that variable related to the regression constant. So that we could include, and easily interpret, factors related to elevations in the dependent variable we re-ran the analysis and requested that a constant be excluded. When we did that, relationships to all the other variables changed. This change in the analysis led to things which were not significantly predictive before now being significant.
I have two questions
Generally speaking, does this approach make sense to examine what factors predict elevations in a given dependent variable?
Why would the regression results differ substantially with the constant removed / what does that mean interpretatively for the first (constant included) versus the second (constant excluded) model.
Thank you for the help. I apologize if I missed an answer to this elsewhere. I had no luck with search.