# Multiple Regressionas a Decision Modeling Technique

Multiple Regression as a Decision Modeling Technique
Herbert M Barber, Jr, PhD, PhD
Xicon Economics

Multiple regression is a relatively simple statistical technique that can be used to make predictive decisions using one continuous dependent variable and two or more independent variables, with the independent variable usually being continuous, or some form of categorical variable that is coded. The technique can be used for many type analyses, I suppose, but as presented here, we will use multiple regression as a tool for developing models through which we render decisions. That said, know that multiple regression is merely an extension of simple linear regression, so if you understand simple linear regression, you should easily be able to add multiple regression to your mix of analytical tools.

As with most statistical and econometric analyses, multiple regression comes with certain assumptions. Foremost, there must be a relationship between the dependent variable and the independent, or predictive, variables. Next, the regression residuals must be homoscedastic and normally distributed. In other words, homoscedasticity distributions share common correlations or covariances. However, multiple regression assumes that the independent variables are not overly correlated—or that there is an absence of multi-collinearity—though in practice this sometimes is a difficult assumption to meet. Nonetheless, in its most fundamental form, multiple regression attempts to fit a single line through scattered data from our variables in an effort of allowing us to determine, or conduct, a few basic items of importance in terms of decision making. First, multiple regression allows us to loosely test the line of best fit, using R2, or R2adjusted. As a point of note, R2, or the coefficient of determination, depicts the variance explained in the independent variable by the dependent variable(s); and R2adjusted is merely a modified form of R2 based upon the number of independent variables in the model. R2 can be determined by squaring multiple R, or the correlation coefficient, while R2adjusted can be determined using a simple equation….

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