REGRESSION ANALYSIS

(Statistics) Mathematical procedures for attributing the variability of one quantity to changes in one or more other quantities. Often called "line fitting" or "curve fitting" since it produces an equation that can be used to predict the quantity of interest under many conditions. The concept is to attempt to fit a mathematical function to a series of data whereby the square of the error terms measuring the differences between the model estimates and actual observations is minimized, hence the term Ordinary Least Squares (OLS) is also used to describe this process. The standard of regression model is generally termed the Classical Linear Regression (CLR) Model. The CLR Model has five basic assumptions: (1) Linearity: The dependent variable, or the variable to be explained or forecasted, can be calculated as a linear function of a specific set of independent, or explanatory variables; (2) Randomness of Disturbance Terms: The expected value of the disturbance term, that is the term showing the differences between the model's estimated values and the actual observed values, is zero; (3) Uncorrelated Disturbance Terms: The disturbance terms all have the same variance and are not correlated with each other (see Serial Correlation); (4) Data Conformity: The observations on the independent variable can be considered fixed in repeated samples, i.e., it is possible to repeat the sample with the same independent variables; (5) Sample Size and Selection: The number of observations is greater than the number of independent variables and that there are no linear relationships, i.e., no significant correlations, between the independent variables (see Multicollinearity).