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.

Some properties of logarithms and exponential functions that you may find useful include: 1.log(e) = 1 2.log(1) = 0 3.log(xr) = r log(x) 4.logeA = A With valuable input and edits from Jouni Kuha. 1The bivariate case is used here for simplicity only, as the results generalize directly to models involving more than

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