Your main tools will be the t-test, the F-test, and adjusted R2. 1. The purpose of this exercise is to obtain the coefficients of X1 and X2 for use in a ceteris paribus (all other conditions the same) analysis. These variables must be included in the analysis. 2. Currently, we do not have a formal test of whether or not the dependent variable should be in levels or logs. However, it is known that X3 explains much of the variation in Y and seems to be uncorrelated most other possible regressors, as you can easily see from the correlation matrix. You should do a scatter plot of Y on X3, Y on log(X3), log(Y) on X3 and log(Y) on log(X3) and see which one seems most linear. 3. X4, X5, and X6 are all correlated with X1 or X2, or both. This means that if any of these should be in the regression, but are omitted, then the results will be biased. Since both X1 and X2 must be in the specification, you might want to test which of these should be in the regression early in your analysis. 4. For X7 and X8, theory tells us that if either of these variables enter the specification, then they both should be in the specification. Also, either both enter in levels or both enter in logs. You might want to do a joint test of these variables. These variables are also correlated with X1 or X2. 5. X9, X10, and X11 are highly correlated. This is because they are different measures of the same object (think about CPI inflation, PCE inflation, core PCE inflation, etc.). At most one of these will enter the specification.
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