Wooldridge PPT ch6

Fall 2008 under econometrics prof keunkwan ryu 16

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Unformatted text preview: Fall 2008 Under Econometrics Prof. Keunkwan Ryu 16 Adjusted R-Squared (cont) It’s easy to see that the adjusted R 2 is just (1 – R 2 )( n – 1) / ( n – k – 1), but most packages will give you both R 2 and adj- R 2 You can compare the fit of 2 models (with the same y ) by comparing the adj- R 2 You cannot use the adj- R 2 to compare models with different y ’s (e.g. y vs. ln( y )) Fall 2008 Under Econometrics Prof. Keunkwan Ryu 17 Goodness of Fit Important not to fixate too much on adj- R 2 and lose sight of theory and common sense If economic theory clearly predicts a variable belongs, generally leave it in Don’t want to include a variable that prohibits a sensible interpretation of the variable of interest – remember ceteris paribus interpretation of multiple regression Fall 2008 Under Econometrics Prof. Keunkwan Ryu 18 Goodness of Fit (cont) Using Adjusted R-Squared to Choose between Nonnested Models Controlling for Too Many Factors in Regression Analysis Adding Regressors to reduce the Error Variance Fall 2008 Under Econometrics Prof. Keunkwan Ryu 19 Standard Errors for Predictions Suppose we want to use our estimates to obtain a specific prediction? First, suppose that we want an estimate of E( y|x 1 =c 1 ,…x k =c k ) = θ = β + β 1 c 1 + …+ β k c k This is easy to obtain by substituting the x ’s in our estimated model with c ’s , but what about a standard error? Really just a test of a linear combination Fall 2008 Under Econometrics Prof. Keunkwan Ryu 20 Predictions (cont) Can rewrite as β 0 = θ – β 1 c 1 – … – β k c k Substitute in to obtain y = θ + β 1 ( x 1- c 1 ) + … + β k ( x k- c k ) + u So, if you regress y i on ( x ij- c ij ) the intercept will give the predicted value and its standard error Note that the standard error will be smallest when the c ’s equal the means of the x ’s Fall 2008 Under Econometrics Prof. Keunkwan Ryu 21 Predictions (cont) This standard error for the expected value is not the same as a standard error for an outcome on y We need to also take into account the variance in the unobserved error. Let the prediction error be ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] { } 2 1 2 2 2 1 1 ˆ ˆ...
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Fall 2008 Under Econometrics Prof Keunkwan Ryu 16 Adjusted...

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