This chapter illustrates the steps one must go through to develop (discover?) an appropriate multiple regression model. I ask that you read it and attempt to understand the pattern of what is being done. Once you have read the chapter, think about the analysis protocol used here. This is an example of higher-order thinking in model building. The previous chapter gave you the computational pieces. This chapter attempts to help you put them together into an analysis strategy.

All this chapter is about is developing strategies for model building using the F-test of a subset of predictors presented on page 658. One strategy is the All Possible Regression approach, where you examine all regression models using all possible subsets of predictors. Once the number of predictors gets large (say greater than 7), the all possible regression approach produces too much information (7!=5040 possible models) for you to effectively utilize in finding the best model. Other strategies are offered: Best Subsets Regression, Forward Selection, Backward Selection, Stepwise Selection.

Even with these model selection strategies there are other issues that need addressing. Should any of the variables be transformed? Which derived variables should be used? There are few good answers to these questions that hold for all situations.

Next we have to assess model assumptions. Again, this is not as easy to do as with simple linear regression, but the basic tools are the same. Outlier detection (a.k.a. finding influential observations) is especially difficult to do in multiple regression. There is a whole range of statistical tools developed specifically to help with outlier detection that are not covered in this book.