Glossary of Statistical Terms

adjusted R-square Since we can raise R2 to 1.0 simply by adding more predictor variables to the regression model, we want to be sure that the predictor variables we do add are statistically significant and, in fact, improve the goodness of fit of the model. Thus, another goodness-of-fit measure known as adjusted R2 has been suggested that accounts for the number of predictor variables included in the regression model. If we add statistically insignificant predictor variables to the model, we would expect to see adjusted R2 decrease for the same reasons described in Chapter 3. Therefore, a predictor variable with an absolute t-statistic greater than 1 will increase adjusted R2 as well as lowering the standard error of the estimate.

alternative hypothesis The alternative hypothesis, Ha, is a statement of what a statistical hypothesis test is set up to establish. For example, in a clinical trial of a new drug, the alternative hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug. We would write Ha: The two drugs have different effects, on average. The alternative hypothesis might also be that the new drug is better, on average, than the current drug. In this case we would write Ha: The new drug is better than the current drug, on average. The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either “Reject H0 in favor of Ha” or “Do not reject ...

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