the method of relative weights, Illiteracy has the greatest relative importance, followed by Frost, Population, and Income, in that order.

Listing 8.17 Applying the relweights() function

>states <- as.data.frame(state.x77[,c("Murder", "Population", "Illiteracy", "Income", "Frost")])

>fit <- lm(Murder ~ Population + Illiteracy + Income + Frost, data=states)

>relweights(fit, col="blue")

Weights

Income 5.49

Population 14.72

Frost 20.79

Illiteracy 59.00

Relative-importance measures (and, in particular, the method of relative weights) have wide applicability. They come much closer to our intuitive conception of relative importance than standardized regression coefficients do, and I expect to see their use increase dramatically in coming years.

8.8Summary

Regression analysis is a term that covers a broad range of methodologies in statistics. You’ve seen that it’s a highly interactive approach that involves fitting models, assessing their fit to statistical assumptions, modifying both the data and the models, and refitting to arrive at a final result. In many ways, this final result is based on art and skill as much as science.

This has been a long chapter, because regression analysis is a process with many parts. We’ve discussed fitting OLS regression models, using regression diagnostics to assess the data’s fit to statistical assumptions, and methods for modifying the data to meet these assumptions more closely. We looked at ways of selecting a final regression model from many possible models, and you learned how to evaluate its likely performance on new samples of data. Finally, we tackled the thorny problem of variable importance: identifying which variables are the most important for predicting an outcome.

In each of the examples in this chapter, the predictor variables have been quantitative. However, there are no restrictions against using categorical variables as predictors as well. Using a categorical predictor such as gender, treatment type, or manufacturing process allows you to examine group differences on a response or outcome variable. This is the focus of our next chapter.