You have a hot grill and an empty hamburger bun, but you have sworn off greasy hamburgers. Would a meatless hamburger do? The data in the table record a flavor and texture score (between 0 and 100) for 12 brands of meatless hamburgers along with the price, number of calories, amount of fat, and amount of sodium per burger. Some of these brands try to mimic the taste of meat, while others do not. The MINITAB printout shows the regression of the taste score y on the four predictor variables: price, calories, fat, and sodium.

MINITAB output for Exercise 13.12

a. Comment on the fit of the model using the statistical test for the overall fit and the coefficient of determination, R².

b. If you wanted to refit the model by eliminating one of the independent variables, which one would you eliminate? Why?

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Brand Score, y Price, x1 Calories, x2 Fat, x3 Sodium, x4 70 91 110 4 310 45 68 90 420 43 92 80 280 41 75 120 370 39 88 90 410 140 30 67 4 440 68 73 120 4 430 56 92 170 6 520 40 71 130 4 180 10 34 67 110 2 180 11 30 92 100 1 330 12 26 95 130 2 340 Regression Analysis: y versus x1, x2, x3, x4 The regression equation is y = 59.8 + 0.129 xl - 0.580 x2 + 8.50 x3 + 0.0488 x4 Coef Predictor Constant SE Coef 59.85 35.68 1.68 0.137 х1 0.1287 0.3391 0.38 0.716 x2 -0.5805 0.2888 -2.01 0.084 х3 8.498 3.472 2.45 0.044 x4 0.04876 0.04062 1.20 0.269 S = 12.7199 R-Sq = 49.9% R-Sq (adj) = 21.3% Analysis of Variance Source DF MS Regression Residual Error 4 1128.4 282.1 1.74 0.244 1132.6 161.8 Total 11 2261.0 Seq ss 11.2 Source DF х1 x2 19.6 x3 864.5 х4 233.2