LINEAR MODEL

(INHERENTLY) (Statistics) Regression Models which can be expressed in a linear form by an appropriate transformation of the Variables. It is this transformation, as represented by the model's Parameters, or Coefficients, that determines the linearity of the model. For example, the model Y = ß2X2 + ß3X3 + ... + ßnXn + e; is inherently linear because it is linear with respect to the coefficients ß2, ß3, ..., ßn. Other transformations resulting in inherently linear models are as follows: Polynomial Model: Y = ß1 + ß2X2 + ß3X22 + e; Log-Log Model: log Y = a1 + a2 log X2 + a3 log X3 + e; Multiplicative Model: Y = ð1X2ð2X3ð3e; Exponential Model: Y = exp (ß1 + ß2X2 + ß3X3) • e; Reciprocal Model: Y = 1/(ß1 + ß2X2 + ß3X3 + e); Semilog Model: Y = ß1 + ß2 log X2 + e