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I have data frame in which I would like to analyse the correlation between academic prestige (factor analysis scores) and public visibility. These scatter plots reveal different patterns in the relationship by different categorical variables

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My question is the following. According to these patterns shown in the graphs, which inference model will analyse the relationship better?

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I would just start with a linear regression explaing news_95 with academic95 title and the interaction between academic95 and title. I suspect a linear effect for the three groups would be fine, but use the usual diagnostics to make sure. The residuals will probably be problematic, so consider using robust standard errors.

Alternatively, if news_95 is a count you could use one of the count models like Poisson regression.

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  • $\begingroup$ news_95 values seem to be limited to the interval (0, ~68) and possibly both variables seem to be discrete. Why do you believe linear regression to be fine? $\endgroup$ – Roland Jan 18 '16 at 12:27
  • $\begingroup$ Just from eyeballing the graph, I don't expect the bounds to bite too much. tzipy still needs to run her or his model diagnostics after estimating the model, but I suspect her model will be good enough. In general, I don't worry too much about a model being "right", as all models are by definition a simplification of reality and thus strictly speaking wrong. The purpose of models is to provide a meaningful simplification of reality, so you need to focus on the model being good enough rather than right. $\endgroup$ – Maarten Buis Jan 18 '16 at 13:45
  • $\begingroup$ I used linear regression but it "failed" the diagnostics because of the extreme a-symmetrical destributions (right skewd) of the variables. then I tried to cunduct a quasi-poisson regression (because of over-dispersion) but none of the categorical variables were significant. $\endgroup$ – tzipy Jan 18 '16 at 20:02
  • $\begingroup$ did you include the interaction term or not? $\endgroup$ – Maarten Buis Jan 18 '16 at 20:12
  • $\begingroup$ no I have'nt. just put dummy variables $\endgroup$ – tzipy Jan 18 '16 at 20:28

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