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Advice on what model to use to perform a formal analysis [migrated]

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I am using the data psid from the library faraway and want to investigate the interaction between sex and year. Specifically, as the year increases does gender impact income less?

I've done some preliminary analysis and found that the current data shows women have overall lower income, but a steeper slope, indicating that the answer is possibly yes. Here is the plot.

I now have to do a formal analysis by finding a parsimonious model through model testing. I'm very new to R and I just don't know where to begin, or what model to use, or even how to apply a model to find an answer to this question. How do I check this model is then a good fit?

Any tips or advice?


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