Week 4 Discussion

Multiple Regression

A multiple or multivariate regression is an extension of a bivariate regression, having at least two

independent variables. This method of regression is used when one independent variable is

inadequate to explain the relationship between the dependent variable and the independent variable.

While employing this method, it is important to use a correct model for analyzing data because a model that is missing necessary independent variables can lead to results that are ambiguous.

Similarly, a model that has additional (unnecessary) independent variables can behave erratically,

especially if the additional independent variable is moderately or highly correlated with some other

independent variable. For this reason, care must be taken to examine the results of a multivariate

regression, to ensure that the model represents the relationship between the dependent variable and

the independent variables as thoroughly and as effectively as possible.

Statistical software packages are sometimes used in order to analyze a multivariate regression, and

the output from such a statistical analysis is useful for examining the degree to which the model is

complete or burdened with unnecessary independent variables. However, a multiple regression can be

alsoestimated with Microsoft Excel.

In order to measure the overall �t of a regression, an F test is utilized. Data from the analysis of

variance (ANOVA) table (the output of the regression) can be used to calculate the F test. An adjusted

coef�cient of determination (adjusted R2) can also be used to measure the overall �t of a regression. In addition, the regression should be tested for nonlinearity. To measure non-quantitative variables, you

can use dummy variables in a regression.