UNIT 4: TRANSFORMATIONS OFVARIABLES CONTENTS 2.4.1.0 Introduction 2.4.2.0 Objectives 2.4.3.0 Main Content 2.4.4.0 Summary 2.4.5.0 Conclusion 2.4.6.0 References/Further Reading 2.4.1.0 INTRODUCTION In model transformation, the functional form of an equation or model determines the estimation techniques and interpretation of results obtained from it. Transforming a variable involves using mathematical procedure to modify its measured values. Single equation (or any other form of equation) maybe indifferent forms. There are two kinds of transformations and generally, models can be of the form i. Linear transformation this preserves the linear relationships between variables parameters and variables are linear. That is the correlation between xand y say) would be unchanged after a linear transformation. Examples of a linear transformation to variable x would be multiplying xby a constant, dividing x by a constant, or adding a constant to x. ii. Nonlinear transformation A nonlinear transformation changes (increases or decreases) linear relationships between variables and, thus, changes the correlation between variables. Examples of a nonlinear transformation of variable x would betaking the square root of x or the reciprocal of x. By extension, nonlinear transformation is a nonlinear model that can be made linear. For example
t u t t Y AX e is an example of production function that can be made linear by taking logarithms, that is ln ln ln t t t Y A X u
