# Regression model comparison query - AIC suggesting a non-significant model is better than an alternative significant model

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!

• what are the AIC values? What's R2, the raw or the adjusted $R^2$? You should obviously look at the adjusted $R^2$. Mar 27 at 14:01
• 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 Mar 27 at 14:10

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.