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I'm learning about regression at university and I really strugging to find good sources to understand the process of model analysis. I have this model below. I'm trying to make the best fitting model with the correct number of predictors.

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So there we have the summary. I have a few questions here. 1) I see the age20-24 is significant, but age25-29 is not. Now the base level is age15-19. So for factors of multiple levels, tell if this is a true statement: "If at least one of the levels of the factor is significantly different from the base case, then we have to keep the age as a variable" - would this be correct?

Also, I'm trying to get the most appropriate model. I'm not sure how to start, but I just started with all the potential predictors. Now I see that Sex is not significant, i'm going to redo the model without sex in it? Is that the kind of process I should follow?

From what I have read, the ratio of ResDev/DF is an indicator of goodness of fit. If it's too big, it could mean overdispersion, OR, it could be that there are other variables out there that should be in the model to explain the increasing variance? So in this case, what should I do now? I think the first step is eliminate all insignificant predictors, and then look at model fit/dispersion.

Help would be much appreciated. Thanks.

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