The model using 12 squared and interaction variables has the smallest s. However, if we desire a somewhat simpler model, note that s does not increase substantially until we move from a model having seven squared and interaction variables to a model having six such variables. Moreover, we might subjectively conclude that the s of 210.70 for the model using 7 squared and interaction variables is not that much larger than the s of 174.6 for the model using 12 squared and interaction variables. Using the fact that the unexplained variations for these respective models are 532,733.88 and 213,396.12, perform a partial F-test to assess whether at least one of the extra five squared and interaction variables is significant. If none of the five extra variables are significant, we might consider the simpler model to be best.
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