Confidence in Regression Results

Interval Estimates and Confidence Criteria Used to Evaluate Regression Output Four criteria can be used to evaluate regressions: • Plausibility • Goodness of fit • Confidence • Specification tests 1. Plausibility The regression model should be plausible. Regression analysis measures only the presence or absence of statistical correlation between a dependent variable and one or more independent variables. Regression analysis cannot conclude that a physical or causal relationship exists between variables. Instead regression analysis should be used to confirm or reject beliefs that have been developed from a study of an underlying process. Many students question the need for, and the relevancy of, determining plausibility. They argue: Why does it matter that we do not really understand the nature of the statistical relationship that we have found? If the rise and fall of the stock market is found to be correlated with some other physical phe-nomenon, such as skirt hemlines, why not use that relationship? If, after careful study, we cannot understand the nature of the rela-tionship, it could be a statistical fluke due to a spurious correlation in the data. If it is a statistical fluke, the relationship could end at any time and without warning. It would be risky to rely on an implausible correlation when attempting to predict or control future activities. 2. Goodness of Fit The goodness-of-fit criterion requires measures of how well the model explains the behavior of the dependent variable. The most common goodness-of-fit measure is the regression coefficient of determination, or R° sta-tistic, discussed in the Chapter 4. The adjusted R' statistic provides a rough indication of whether adding additional independent variables has increased the explanatory power of the model. 3. Confidence Conidence concerns the statistical confidence, or relatity, that we can place in the regression results, Tics confecticients rehendon result cance interest the statistics of the deficiend sor the independent vanbecome use intervals can also be developed for predictions from the regression model, as explained in Chapter 4. 4. Specification Tests Specification tests are undertaken to ensure that the critical assumptions of regression have been met in a particular application.