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3. Oehlert provides data from a small experiment with n = 16 observations on baking packaged cake mixes. Two factors, X1 = baking time in minutes and X2 = baking temperature in degrees F, were varied in the experiment. The response Y was the average palatability score of four cakes baked at a given combination of (X1, X2), with higher values desirable. We fit the full second model Model I: Yi = Bo + Bixa + Box:2 + Bligh + 822x32 Model II: Yi = Bo + B20:2 + 322032 Model III: Yi = Bo + Bixa + Box:2 + Buch + 822x12 + Bizxax:2 ## Test for model II and model III > f2.1m = 1m (Y X2+I(X2-2) , data = cake) > f3.1m = 1m(Y X1+X2+I (X1 2)+I(X2-2)+X1 : X2, data = cake) > anova (f2. Im, f3. 1m) Analysis of Variance Table Model 1: Y ~ X2 + I(X2-2) Model 2: Y ~ X1 + X2 + I(X1-2) + I(X2-2) + X1:X2 Res . Df RSS Df Sum of Sq F Pr (>F) ? 14.4380 N P 2.7525 ? ? ? * * * Signif. codes: ( '***' 0.001 '**' 0.01 * *' 0.05 '. ' 0.1 ' > 1 (a) (8 points) For the model I, the residual standard error is o = 0.7289. Given the R-squared value R" = 0.8125, solve SSTO. Fill in the ANOVA table for Model I, and test the hy- pothesis that this model is useful. Source SS df MS F Regression Residual Total (b) (5 points) What is the hypotheses test of the ANOVA table in the R output? What is the F-test statistics and conclusion? Use a = 0.01. (c) (4 points) Compute both the AIC and BIC criteria for model II and model III. Which model does each criterion suggest you should use? (Note: use the natural logarithm for AIC and BIC formulas)