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I currently have a log-log model. Its scatter plot looks like this: enter image description here

I am currently stuck after this. I need to find a non-linear relationship to predict how log (X Variable) will affect log (Y Variable). Would simply using this log-log model be enough to predict? Or would I need to manipulate the model further by adding another term such as a squared log(x variable) term, much like in a quadratic model?

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  • $\begingroup$ Welcome to the site. Can you clarify why you would "need to find a non-linear relationship to predict how log (X Variable) will affect log (Y Variable)?" Is this part of a class assignment that specifically asked for it? $\endgroup$
    – Marquis de Carabas
    Commented Apr 16, 2016 at 4:41
  • $\begingroup$ Yes, the class assignment specifically asked for it. $\endgroup$
    – ConfusedUndergraduate
    Commented Apr 16, 2016 at 4:42
  • $\begingroup$ Since this is a class assignment, please add the self-study tag $\endgroup$
    – Marquis de Carabas
    Commented Apr 16, 2016 at 13:53

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I think you should try to fit a polynomial regression because your data looks like a shaped distribution. Once you fit polynomial, you may want to compare it with the linear regression by likelihood-ratio test to convince yourself that your polynomial fitting is worth the loss of one or more degrees of freedom. Your polynomial model will always fit no worse than a simple linear model, the likelihood-ratio test will tell you whether it'd be a good idea to do so.

From the plot, it looks like a second-order polynomial should be sufficient.

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