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Wondering if anyone can help. I’m trying to compare two regression models with one predictor to see which best describes the data.

Model one is a linear model (y = ax + b) with R2 = .036, F = 3.047, p =.084

Model two is a reciprocal quadratic model (y = a(1/x)2 + b(1/x) + c) with R2 = .072, F = 3.128, p =.045

As you can see, neither fit the data that well, although model two is just about significant. As model one approached significance, and had fewer parameters, I used Akaike’s Information Criterion to compare the two models, with AIC suggesting that model one is more likely to be correct.

I’m a little confused as to how I should interpret this. Should I consider that model one is more likely to represent the data, even though it is not significant, or should I consider model two as a better fit because it has a larger R2 and is significant?

Any help is appreciated!

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    $\begingroup$ what are the AIC values? What's R2, the raw or the adjusted $R^2$? You should obviously look at the adjusted $R^2$. $\endgroup$
    – utobi
    Mar 27 at 14:01
  • $\begingroup$ Ah, the R2 values reported above are raw R2. Here’s the adjusted R2 and AIC values for each model: Model one: Adjusted R2 = .024 AIC: -242.846 Model two: Adjusted R2 = .049 AIC: -156.231 $\endgroup$
    – analogicalmind
    Mar 27 at 14:10

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In both cases, the portmanteau $F$-tests are at the margins of the significance level and the adjusted $R^2$ are pretty small. The message IMO is that those models are doing a pretty bad job.

However, if you really have to choose one, then, since the models are not nested and have a different number of parameters, I would choose on the basis of the AIC (or BIC if that matters). In this case, there is a discrepancy of AICs equal to 86.615 in favour of the simpler model. Thus the AIC suggests picking the first model.

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  • $\begingroup$ Very helpful. Much appreciated. $\endgroup$
    – analogicalmind
    Mar 27 at 14:25

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