A statistical program is recommended. An article gave the data, shown in the table below, on dimensions of 27 representative food products. Product Material Height 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 glass glass glass glass plastic glass glass plastic plastic plastic tin plastic glass glass glass glass cardboard cardboard glass glass glass glass glass glass plastic tin tin 7.7 6.2 8.5 10.4 OH₂A₁B₂B₂=0 8.0 8.7 10.2 10.5 3.4 6.9 10.9 9.7 10.1 13.0 13.0 11.0 8.7 17.1 16.5 16.5 9.7 17.8 14.0 13.6 27.9 19.5 13.8 Maximum Width 2.50 2.90 OH: at least one of ₁, ₂ or B, is not 0 H₂: A₁-A₂ =B₂ = 0 2.15 OH: A₂ and , are all not 0 H₂: A₁-A₂=₂=0 2.90 3.20 2.00 1.60 4.80 5.90 5.80 2.90 2.45 2.60 2.60 2.70 3.10 5.10 10.20 3.50 2.70 3.00 2.70 2.50 2.40 4.40 7.50 4.25 Minimum Width (c) Carry out a model utility Ftest at a 0.05 significance level. State the null and alternative hypotheses. B₂ =B₂ = 0 OH₂ B₁ H: ₂ and , are all not 0 H: at least one of ₁.₂ or ₂ is not 0 1.80 2.70 2.00 2.60 3.15 1.80 1.50 3.80 5.00 4.75 2.80 2.10 2.20 2.60 2.60 2.90 5.10 10.20 3.50 1.20 1.70 1.75 1.70 1.20 1.20 7.50 4.25 Elongation Volume 1.50 1.07 1.98 1.79 1.25 2.17 3.19 1.09 0.29 0.59 1.88 1.98 1.94 2.50 2.41 1.77 0.85 0.84 2.36 3.06 1.62 3.30 2.80 2.83 (b) Why should we consider adjusted R² instead of R² when evaluating this model? O We should consider the adjusted O We should consider the adjusted O We should consider the adjusted O We should consider the adjusted instead of instead of instead of instead of 3.17 1.30 1.62 130 139 Calculate the test statistic. (Round your answer to two decimal places.) F= Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value= 180 281 332 93 119 515 325 568 339 180 235 239 363 312 631 1248 651 306 320 (a) Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score. (Round your numerical values to two decimal places. Use x, for minimum width, x, for the maximum width and x, for the elongation score.) ŷ = 310 247 204 1204 2329 731 because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably less than ². because it does not take into account the number of predictors used in the model. In this case the adjusted is noticeably greater than ². because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably greater than ². because it does not take into account the number of predictors used in the model. In this case the adjusted is noticeably less than ². What can you conclude? O Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of ₁.₂ or ₂ is not 0. O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that ₁, ₂ and S, are all not 0. O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of ₁, ₂ or ₂ is not 0. O Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁₂ and , are all not 0.