Linear Regression Models with Logarithmic Transformations

Linear Regression Models with Logarithmic TransformationsKenneth Benoit Methodology InstituteLondon School of 17, 20111 Logarithmic Transformations of variablesConsidering the simple bivariate Linear modelYi= + Xi+ i,1there are four possible com-binations of Transformations involving logarithms: the Linear case with no Transformations , thelinear-log model , the log- Linear model2, and the log-log Yi= + Xi Yi= + logXilogYlog-linearlog-loglog Yi= + Xilog Yi= + logXiTable 1: Four varieties of Logarithmic transformationsRemember that we are usingnaturallogarithms, where the base ise Logarithms mayhave other bases, for instance the decimal logarithm of base 10.

24 68 0 20 40 60 80 100 Log(Expenses) 3 Interpreting coefficients in logarithmically models with logarithmic transformations 3.1 Linear model: Yi = + Xi + i Recall that in the linear regression model, logYi = + Xi + i, the coefficient gives us directly the change in Y for a one-unit change in X.No additional interpretation is required beyond the

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