So continuing in a little less than ideal fashion because there was a lot of painstaking research that I did on the data by performing various different tests. However my system crashed so I will try to replicate what I can and remember.
I had reached a bit of a dead end with the data wondering why I was really trying to model diabetes on the basis of inactivity and obesity.
In a way I had set out with a goal in mind to look for and had spent all my time looking for it, when the fact is that it may not necessarily even exist.
So I was comparing how the fits are when the models are built from a different set of predictors and what is the value to be predicted.
In doing these tests, I was finding that the multiple linear model of diabetes and obesity, for predicting inactivity was giving the highest R squared term I had encountered so far of 0.42. Actually it was 0.39 for a linear model which was much higher than any other previous linear model I had encountered, and it jumps to 0.42 with the addition of the interaction term.
This was particularly interesting because transformations did not help better the correlation but instead worsened it, in nearly all cases where the model was made more complex, such as log or polynomials.
However when I was comparing test errors for this, using K fold cross validation this model produced an error much higher than that of the 0.3 seen in the log models.