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The Algebra of a Class of Transformations with Applications to Log-Log Models of School Spending

A transformation is defined and algebraic relatconships developed between the least squares coefficients, standard errors, and R2 in the original and transformed models. This complete analysis is then used to explain the impact on these quantities of different measures of the tax price and dependent variable in log-log school spending models. More generally, it is shown that the different specifications are linked to each other through this transformation so that they have a common fundamental structure. The results should be interpreted in this light. Other applications are described briefly.