So after finalizing all the analysis based on the assumption that the relationships between my predicted variable and the predictors are linear (which was concluded based on looking at the scatter plots and 'fitting' a straight linear line which generally gathered the cases around it, my variances are also all homoscedastic as well), I discovered through what is called curve estimation that I could also fit a nonlinear line and I tried both quadratic and cubic. To my surprise, they both returned an R-square very close (a bit higher but I am aware about the possibility of over-fitting) than the original linear one but the F test value is always the highest for the linear model. What does this suggest?
- Does it mean that the relationships between my variables are not only linear? In other words, does this violate the assumption of multiple linear regression?
- Am I obligated to report the non-linear relationships?