Lecture Notes on Regression Analysis (Part 1)

Abstract

The term regression was first used by the English statistician Sir Fransis Galton. He related the length of fathers to the length of their sons. He discovered a regression such that tall fathers mostly have tall sons, However the sons were on an average not as tall as the fathers, Further small fathers had on an average small sons, but on an average not as small as they were. Thus there was a regression to the average. Before we can enter the field of regression analysis we have to specify the variables we want to use. This is done in economic theory. After finding the variables we have to draw a scatter diagram in order to be able to find the mathematical form of the relation which suits best to the matter. E.g. if the scatter takes a linear form we use a linear relation. If the relation shows curved properties we may use a double logarithmic form. One should realise however that economic theory should also give an indication about the form of the relation. Next we can apply certain regression techniques to find a numerical specification of the unknown. coefficient Here it does not matter much if we either have a linear form (y = a + bx) or a non-linear form (ln y = ln a + b ln x) and the coefficients a and b can be specified by using ln x and ln y instead of x and y as variables in the regression. In Section 2 a distinction will be made between different economic relations. In the third section we shall present a sample of possible mathematical forms of the relation. The fourth section is engaged in drawing a scatter diagram. In the fifth section the techniques of regression analysis will be explained. In the last part of this memo. example is presented. The computation of the Pareto constant for the income distribution was chosen because many practical difficulties are faced.