The Four Potential Models

Recalling the original generic model specification, and substituting in the specific control variable functions explained above, we now have:

Current Per-Pupil Spending =
      b0 + â * {f(Size), ln(FedRevenuesPP), FedRevenuesPP²,
      StateLunchRevPP, StateLunchRevPP², ln(PctSpecialEd),
      ln(PctWhite), EnrollmentByPopulation², IncomePerCapita,
      IncomePerPupil², MedianHouseAskingPrice,
      MedianHouseAskingPrice², MedianRentAsked²,
      [Years]} + error

Combining this formula with the four different specifications for the f(Size) function discussed in the preceding section, we arrive at four different completed specifications, where f(Size) in the generic model is defined in one of the following ways:

(1)   ƒ(Size) = Size                              (Linear)
(2)   ƒ(Size) = ln (Size)                        (Logarithmic)
(3)   ƒ(Size) = a * Size + Size²              (Quadratic)
(4)   ƒ(Size) = ln2 (Size) − a * ln (Size)   (Checkmark)