Question: ( 4+4+7+6+6=27 points ) Use the "BrandPreference" dataset. Here, n = 16 observations are used to develop an equation for estimating Y = Degree of brand liking from X ₁ = Moisture content of the product and X ₂ = Sweetness of the product. The results were obtained from an experiment based on a completely randomized design (the data is coded).

1. Obtain the studentized deleted residuals and identify any outlying Y observations using the Bonferroni outlier test procedure with α = 0.10. (See page 396: Test for Outliers for details.) State the decision rule and your conclusion. [In Minitab: Use "Storage" and check "Deleted residuals" under "Stat > Regression > Regression > Fit Regression Model …" to get studentized deleted residuals.]
2. Use the leverage values to explain if any of the observations are outlying with regard to their X-values according to the rule of thumb 3(p/n).
   [In Minitab, use "Storage" and check "Leverages" under "Stat > Regression > Regression > Fit Regression Model …" to get leverage values.]
3. Management wishes to estimate the mean degree of brand liking for moisture content X ₁ = 10 and sweetness X ₂ = 3. Construct a scatterplot of X ₂ against X ₁ and determine visually whether this prediction involves an extrapolation beyond the range of the data. Also, use equation (10.29) in the textbook with to determine whether an extrapolation is involved (you’ll need to employ matrix methods to do the calculations needed). Do your conclusions from the two methods (the scatterplot and the equation) agree?
4. The largest absolute studentized deleted residual is for case 14 (see part (a)). Obtain the DFFlTS and Cook's distance values for this case to assess the influence of this case. What do you conclude from each of the DFFlTS and Cook's distance values?
5. Calculate the average absolute percent difference in the fitted values for models with and without case 14. What does this measure indicate about the influence of case 14? [Hint: Store the fitted values for the model that includes case 14 and name them fit1. Delete Y for case 14 from the worksheet, refit the model, store the fitted values , a nd name them fit2. Note that you should have a fitted value for case 14, even though this case wasn’t used to fit the model. Calculate the absolute percent differences between the fitted values, e.g., abs ( 100*(fit2-fit1)/fit1 ) . Then f ind the average of the absolute percent differences. ]

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