Very High R square and significant lack of fit problem

[#1]

Hi,

I made custom design for 7 factors with a model containing main effects, interractions and 2 order powers. Number of sample size is 150. I see that 3 of factors are important and made model for these 3 variables.

However i faced with significant lack of fit problem and 0.99 R^2 value.

I searched a lot about the reasons of this situation but i could not find a clear answer.

Do you have an idea about it, what causes this problem?   

Kind regards.

[#2]

@Ella It seems to me that you have unmodeled mean structure remaining in the residuals. By the looks of it you fit f(X) = a + bX + e and by observation, the model f(X) = a + b1X + b2X^2 + e may provide a better fit? What do you residual look like if you run the latter model?

[#3 · Accepted solution]

Just to re-iterate, R-square by itself must be interpreted carefully.  R-square will always increase as you add DF's to the model.  But the point of creating a model is to include only the useful terms (active and significant).  So you should look at the delta between the R-square and the R-square adjusted.  As the delta increases, it is an indicator your model is over specified.

Looking at your residuals, there is an indication of a non-linear effect.  Your model should consider perhaps adding a quadratic effect as suggested by @modelFit