A model can be significant and explain a lot of variability and still exhibit lack of fit. For example, the model may be missing an important term, as shown in the attached simple example.
![Example.PNG Example.PNG](https://community.jmp.com/t5/image/serverpage/image-id/18489i5AE1502CD3670552/image-size/medium?v=v2&px=400)
A significant lack of fit usually indicates that the model form is not correct and usually indicates that there is a curvilinear relationship. Residual plots are the best and easiest tool to use to try and determine why there is a lack of fit. A good residual plot will show random scatter. Any pattern will indicate a systematic problem with your chosen model. For my simple example, here is a residual plot (there is more than one residual plot, so look at all of them to help determine the problem with your model).
![Resid.PNG Resid.PNG](https://community.jmp.com/t5/image/serverpage/image-id/18490i7CC80EBCF435DD07/image-size/medium?v=v2&px=400)
There is an obvious pattern here indicating that I need a quadratic term in the model to estimate the curvature. I THINK this is a problem with your model as well, but the residual plots should help you.
Dan Obermiller