6. [4/9 Points] DETAILS PREVIOUS ANSWERS PODSTAT5 14.E.028. A statistical program is recommended. An article gave the data, shown in the table below, on dimensions of 27 representative food products. Maximum Product Material Height Width Minimum Width Elongation Volume 1 glass 7.7 2.50 1.80 1.50 124 2 glass 6.2 2.90 2.70 1.07 139 3 glass 8.5 2.15 2.00 1.98 171 4 glass 10.4 2.90 2.60 1.79 280 5 plastic 8.0 3.20 3.15 1.25 329 6 glass 8.7 2.00 1.80 2.17 85 7 glass 10.2 1.60 1.50 3.19 118 8 plastic 10.5 4.80 3.80 1.09 515 9 plastic 3.4 5.90 5.00 0.29 332 10 plastic 6.9 5.80 4.75 0.59 572 11 tin 10.9 2.90 2.80 1.88 342 12 plastic 9.7 2.45 2.10 1.98 173 13 glass 10.1 2.60 2.20 1.94 241 14 glass 13.0 2.60 2.60 2.50 236 15 glass 13.0 2.70 2.60 2.41 365 16 glass 11.0 3.10 2.90 1.77 311 17 cardboard 8.7 5.10 5.10 0.85 636 18 cardboard 17.1 10.20 10.20 0.84 1255 19 glass 16.5 3.50 3.50 2.36 652 20 glass 16.5 2.70 1.20 3.06 306 21 glass 9.7 3.00 1.70 1.62 315 22 glass 17.8 2.70 1.75 3.30 310 23 glass 14.0 2.50 1.70 2.80 249 24 glass 13.6 2.40 1.20 2.83 197 25 plastic 27.9 4.40 1.20 3.17 1207 26 tin 19.5 7.50 7.50 1.30 2329 27 tin 13.8 4.25 4.25 1.62 730 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (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 answers to two decimal places. Use x₁ for minimum width, x2 for the maximum width and x3 for the elongation score.) ŷ = x1+ x3 (b) Why should we consider adjusted r² instead of 2 when attempting to determine the quality of fit of the data to our model? We should consider the adjusted 2 instead of 2 because it takes into account the number of predictors used in the model. In this case the adjusted 2 is noticeably less than r². We should consider the adjusted 2 instead of 2 because it takes into account the number of predictors used in the model. In this case the adjusted² is noticeably greater than r². We should consider the adjusted 2 instead of 2 because it does not take into account the number of predictors used in the model. In this case the adjusted r² is noticeably greater than 2. We should consider the adjusted 2 instead of 2 because it does not take into account the number of predictors used in the model. In this case the adjusted r² is noticeably less than 2. (c) Perform a model utility test at a 0.05 significance level. State the null and alternative hypotheses. = = = Ho B1 B2 B3 0 H: B₁, B and B are all not 0 = Ho B1 B2 B3 = 0 H₂: at least one of ẞ₁, B₂ or B3 is not 0 1' Ho: at least one of ẞ₁, B₂ or ẞ is not 0 = = Ha B1 B2 B3 = 0 1' Ho: B1, B2 and B3 are all not 0 = Ha B1 B2 B3 0 Calculate the test statistic. (Round your answer to two decimal places.) F = What can be said about the P-value for this test? P-value 0.100 0.050 P-value < 0.100 0.010 P-value < 0.050 0.001 P-value < 0.010 P-value <0.001 What can you conclude? Reject Ho. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of B1, B2 or ẞ3 is not 0. 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 ẞ3 is not 0. Reject Ho. We have convincing evidence that the multiple regression model is useful and can conclude that B₁, ẞ2 and ẞ3 are all not 0. Fail to reject Ho. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that B1, B2 and ẞ3 are all not 0. You may need to use the appropriate table in Appendix A to answer this question.