Putting the Statistics Together In sum, there are four important statistics to attend to in a linear regression model. First, the F statistic tests whether the model as a whole predicts the dependent variable. Second, the regression coefficients measure the strength and direction of the relationships. Third, for each of these regression coefficients, there is a significance score, which measures the likelihood that the relationship revealed in the coefficients can be attributed to random chance. Finally, the R-square statistic measures the model’s overall predictive power and the extent to which the variables in the model explain the variation in the dependent variable. In our example, we found that teenage births are positively related to poverty—poorer states have, on average, a higher percentage of births to teenage mothers than affluent states. We also observed that this relationship is unlikely to be due to random chance. Finally, we discovered that poverty has very strong predictive powers, as this one variable accounts for well over two thirds (71.3%) of the variation in teen birthrate within the United States.
