4.6.2.6. Compare the Fits

4. Process Modeling
4.6. Case Studies in Process Modeling
4.6.2. Alaska Pipeline

4.6.2.6. Compare the Fits

Three Fits to Compare

It is interesting to compare the results of the three fits:

Unweighted fit
Transformed fit
Weighted fit

This plot shows that, compared to the original fit, the transformed and weighted fits generate smaller predicted values for low values of lab defect size and larger predicted values for high values of lab defect size. The three fits match fairly closely for intermediate values of lab defect size. The transformed and weighted fit tend to agree for the low values of lab defect size. However, for large values of lab defect size, the weighted fit tends to generate higher values for the predicted values than the transformed fit.

Conclusion

Although the original fit was not bad, it violated the assumption of homogeneous variances for the error term. Both the fit of the transformed data and the weighted fit successfully address this problem without violating the other regression assumptions.

Whether or not it is worth the effort to find a better model is an engineering judgement as well as a statistical judgement. If the application did not require an especially accurate fit, we may have been satisfied to stick with the original model of the untransformed data even though there was a modest violation of one of the regression assumptions. However, if the application required the hightest precision possible, we would benefit from making the extra effort to find the best model possible.