More Than Two Explanatory Variables
More Than Two Explanatory Variables
This chapter shows that the addition of a second explanatory variable in Chapter 11 adds only four new things to what there is to know about regression. First, regression uses only the parts of each variable that are unrelated to all of the other variables. Second, omitting a variable from the sample relationship that appears in the population relationship almost surely biases our estimates. Third, including an irrelevant variable does not bias estimates but reduces their precision. Fourth, the number of interesting joint tests increases with the number of slopes. All four remain valid when we add additional explanatory variables.
Keywords: regression analysis, explanatory variables, population relationship, biased estimates, slopes
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