A statistical program is recommended. An article gave the data, shown in the table below, on dimensions of 27 representative food products. Product 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Material Height glass glass glass glass plastic glass glass plastic plastic plastic tin plastic glass glass glass glass cardboard glass glass glass glass glass glass plastic tin tin 7.7 6.2 8.5 10.4 8.0 O Ho: B₁-B₂-B₂ = 0 8.7 10.2 O Ho: B₁-B₂-B₂-0 10.5 3.4 6.9 10.9 cardboard 17.1 9.7 10.1 13.0 13.0 11.0 8.7 16.5 16.5 9.7 17.8 14.0 13.6 27.9 19.5 13.8 O we should consider the adjusted O We should consider the adjusted O We should consider the adjusted Maximum Width O Ho: at least one of B₁, B₂ or B₂ is not 0 H₂: B₁-B₂-B₂=0 2.50 2.90 2.15 H: B₂B and B, are all not 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 (c) Carry out a model utility F test at a 0.05 significance level. State the null and alternative hypotheses. O Ho: B₁ B₂ and ₂ are all not 0 H₂: B₁-B₂ =B₂ = 0 H: at least one of B₁ B₂ or ₂ is not 0 Minimum Width 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 Calculate the test statistic. (Round your answer to two decimal places.) F = 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 3.17 1.30 1.62 129 137 Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value= 179 289 334 85 120 518 334 573 335 180 235 235 357 314 636 1254 648 (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, x₂ for the r 302 (b) Why should we consider adjusted R² instead of R2 when evaluating this model? O We should consider the adjusted instead of 2 because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably less than ². ² instead of r² because it does not take into account the number of predictors used in the model. In this case the adjusted ² is noticeably greater than ². instead of 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. instead of 2 because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably greater than 2. 320 301 250 195 1201 2325 728 What can you conclude? O Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁, ₂ and 6 are all not 0. 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 3 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 ₂ are all not 0. O Fail to reject Ho- We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of B₁, B₂ or B₂ is not 0.