Question
Consider this simple F2 group ANOVA design with M1 4 and m = 2- SAS DATA AND PROC GLM code: data matz input group; cardsproc g1m data-matz;class group (REE = 2' ) model group;means group run; PROC GLM Output: The GLM Procedure Dependent Variable: Source DF Sum of Squares Mean SquareValue PrModel 0.0705 Error Corrected Total12 0ooo12.00o006.000o00 20.000000000R-Square 600000Coeff Var 28.28427Root MSE 1.414214Mean 5. 0oooooSourceDFType Iii SSMean SquareValuePrgroup 0.070512.0ooooooo12.0oooooo
Consider this simple F2 group ANOVA design with M1 4 and m = 2- SAS DATA AND PROC GLM code: data matz input group; cards proc g1m data-matz;class group (REE = 2' ) model group;means group run; PROC GLM Output: The GLM Procedure Dependent Variable: Source DF Sum of Squares Mean Square Value Pr Model 0.0705 Error Corrected Total 12 0ooo 12.00o00 6.00 0o00 20.0000 00000 R-Square 600000 Coeff Var 28.28427 Root MSE 1.414214 Mean 5. 0ooooo Source DF Type Iii SS Mean Square Value Pr group 0.0705 12.0ooooooo 12.0ooooooo 6. 00 Level of group Mean 0ooooooo 3.0ooooooo Std Dev 1.41421356 1.41421356 Pait 2_ The OLS solution for regression coefficients is b = [Xx]-IXy 2.A. Solve bp = [Xo Xo] IXoy: points) 2.B. What Statistical Entities does the answeer (bp [Xo Xo]-'Xo >) in 2A Equal? (2 points) The Nxl Vector of Predicted values are ? = Xobp 2.C. Solve 2= Xobp poits)
Answers
Use the data set GPAl for this exercise.
(i) Use OLS to estimate a model relating $\operatorname{col} G P A, A C T,$ skipped, and $P C$ . Obtain the OLS residuals.
(ii) Compute the special case of the White test for heteroskedasticity. In the regression of $\hat{u}_{i}^{2}$ on $\widehat{\operatorname{col} G P A}_{i}, \overline{c o l G P A_{i}^{2}},$ obtain the fitted values, say $\hat{h}_{i}$
(iii) Verify that the fitted values from part (ii) are all strictly positive. Then, obtain the weighted
least squares estimates using weights 1$/ \hat{h}_{1}$ . Compare the weighted least squares estimates for the effect of skipping lectures and the effect of PC ownership with the corresponding OLS estimates. What about their statical significance?
(iv) In the WLS estimation from part (iii), obtain heteroskedasticity-robust standard errors. In othe
words, allow for the fact that the variance function estimated in part (ii) might be misspecified.
(See Question $8.4 . )$ Do the standard errors change much from part (iii)?
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