The general linear regression model can be stated by the equation:Īssumptions of the Ordinary Least Squares Regression ModelĮach of these assumptions needs a bit more explanation. There are techniques for overcoming some of these difficulties, exponential and logarithmic transformation of the data for example, but at the outset we must recognize that standard ordinary least squares (OLS) regression analysis will always use a linear function to estimate what might be a nonlinear relationship.
The marginal cost curve, for example, is decidedly nonlinear as is the total cost function, if we are to believe in the effect of specialization of labor and the Law of Diminishing Marginal Product. This presents us with some difficulties in economic analysis because many of our theoretical models are nonlinear. This linearity assumption is required because, for the most part, the theoretical statistical properties of non-linear estimation are not well worked out yet by the mathematicians and econometricians. Regression analysis is based upon a functional relationship among variables and further, assumes that the relationship is linear. This last feature, of course, is all important in predicting future values. Further, regression analysis can provide an estimate of the magnitude of the impact of a change in one variable on another. Regression analysis is a statistical technique that can test the hypothesis that a variable is dependent upon one or more other variables. Linear Regression and Correlation 71 The Regression Equation