# Thread: Correcting lack of fit

1. ## Correcting lack of fit

I have a very simple data set with a single regressor that has all negative values. The data set provides no context, only values.

When testing the linear regression model for lack of fit in SAS, the F-value is over 500 and p-value is <.0001. I am using an alpha of .05.

What would be the best way to proceed when faced with this kind of situation?

2. ## Re: Correcting lack of fit

Have you examined the residuals and/or the scatterplot? Can you identify any potential sources of lack of fit? Can you see a higher order polynomial that might provide a better fit? How large is your sample size?

3. ## The Following User Says Thank You to Dason For This Useful Post:

zicke01 (10-21-2012)

4. ## Re: Correcting lack of fit

Originally Posted by Dason
Have you examined the residuals and/or the scatterplot?
The residuals appear quadratic and the scatter plot has oscillation.

Can you identify any potential sources of lack of fit?
Other than it appearing to be a non-linear relationship, no.

Can you see a higher order polynomial that might provide a better fit?
It appears as though a quadratic model or sine function might fit, but I'm not sure how I'd proceed with this.

How large is your sample size?
The sample size is 82.

By the way, I'm mainly posting here to double check my original conclusion that the linear model is worthless and that there is no reason to test for the assumptions since we need to develop a better model.

5. ## Re: Correcting lack of fit

Well I wouldn't call it 'worthless' but if you see a clear quadratic trend then by all means don't go checking the assumptions for the model you fit and instead fit a quadratic model.

6. ## The Following User Says Thank You to Dason For This Useful Post:

zicke01 (10-21-2012)

7. ## Re: Correcting lack of fit

Originally Posted by Dason
Well I wouldn't call it 'worthless' but if you see a clear quadratic trend then by all means don't go checking the assumptions for the model you fit and instead fit a quadratic model.
The problem is that this is an exam question that is then followed up with checking the assumptions and the construction of confidence intervals for the model.

I'm trying to convince myself that I'm better off explaining how the model isn't worth checking and that some transformation is necessary because that shows a better grasp of the material than just mindlessly testing a poor model, but that would essentially leave the question "unanswered" as far as demonstrating the tests for assumptions and confidence intervals go.

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