I have a problem that I am sure people with more mathematical knowledge may be able to solve fairly easily. I have a simple model I have built between two variables where an exponential relationship exists. I have taken the natural log of my target variable and built a linear model. I am using it to predict on new data. The predictions are fairly accurate on values up to a certain point (probably at the point of the exponential curve where there is still a somewhat linear relationship), but the larger the independent variable, the less accurate the prediction is. This makes intuitive sense (I think) - the farther up the exponential curve the values go, the less accurate the model is going to predict, even when log-transforming.
Is there a way to improve the accuracy on all predictions? Am I approaching this correctly? Can I improve my question? I can also supply an example if that helps. Thank you in advance, this is vexing me.
I have tried segmenting my models out - building a linear model for values under a certain point, and values over a certain point. Naturally the model for the values over a certain point is not as strong.
