Transformations

Abstract

Until now we have considered situations where the algebraic form of the model, i.e.,

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS % baaSqaaiaaicdaaeqaaOGaey4kaSIaeqOSdi2aaSbaaSqaaiaaigda % aeqaaOGaamiEamaaBaaaleaacaWGPbGaaGymaaqabaGccqGHRaWkca % GGUaGaaiOlaiaac6cacqGHRaWkcqaHYoGydaWgaaWcbaGaam4Aaaqa % baGccaWG4bWaaSbaaSqaaiaadMgacaWGRbaabeaakiaacYcaaaa!4937! $${\beta _0} + {\beta _1}{x_{i1}} + ... + {\beta _k}{x_{ik}},$$

was approximately correct. Obviously, this will not always be so. The actual relationship may not be a linear function of the x _ij ’s and sometimes not even of the β _j ’s. In some such cases we may still be able to do linear regression by transforming (i.e., using functions of) the independent and/or the dependent variables.