One approach to building a regression when faced with a large collection of explanatory variables is to use them all. We call this the saturated model because it includes every explanatory variable available. We have 21 possible explanatory variables and, after setting aside the two outliers, 196 observations. With more than 9 observations per explanatory variable, we have plenty of data to fit this regression. (Some statisticians suggest fitting the saturated model so long as you have at least 3 observations per explanatory variable.) If the explanatory variables were nearly uncorrelated, we would be able to interpret this model as well. With the substantial collinearity among these, however, that’s not going to happen. The redundancy ...
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