INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
88 In regression, however, a transformation to achieve linearity is a special kind of nonlinear transformation. It is a nonlinear transformation that increases the linear relationship between two variables.
2.4.2.0 OBJECTIVE The main objective of this unit is to show that regression analysis can be extended to fit nonlinear models through transformation of nonlinear model that can be made linear.
2.4.3.0 MAIN CONTENT
A limitation out of other limitations of linear regression analysis is that it is contained in its very name, in that it can be used to fit only linear equations where every explanatory term, except the constant, is written in the form of a coefficient multiplied by variable
…[2.74]
Y equations such as the two below are nonlinear
1 1
2 X
Y
…[2.75] And
…[2.76] Nevertheless, both [2.75] and [2.76] have been suggested as suitable forms for Engel curves, (the relationship between the demand fora particular commodity, Y and income, X). As an illustration, given data on Y and X, how could one estimate the parameters
in these equations Actually, in both cases, with a little preparation one can actually use linear regression analysis. Here, first, note that [2.74] is linear in two ways. The right side is linear invariables because the variables are included exactly as defined, rather than as functions. It, therefore, consists of a weighted sum of the variables, the parameters being the weights. The right side is also linear in the parameters since it consists of a weighted sum of these as well, the X variables being the weights in this respect.
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