A statistical program is recommended.An article gave the data, shown in the table below, on dimensions of 27 representative food products.Product Material HeightV123456781112131415161718192021222324252627glassglassglassglassplasticglassglassplasticplasticplastictinplasticglassglassglassglasscardboardcardboardglassglassglassglassglassglassplastictintin7.76.28.510.48.010.2ⒸH₂ : B₁ = B₂ =B₂ = 010.53.46.910.99.710.113.013.011.08.717.116.516.517.814.013.627.919.513.8OH:₁₂ and B, are all not 0H₁₂P₁ =B₁₂ =B₂ = 0MaximumWidthHB₁ B₂ and ₂ are all not 02.50OH: at least one of B₁, B₂, or is not 0H₁₂ : B₁ =B₁₂= B ₂ = 02.902.15H₂: at least one of B₁, B₂ or B₂ is not 02.903.202.001.604.805.905.802.902.452.602.602.703.105.1010.203.502.703.002.702.502.404.407.504.25MinimumWidth(c) Carry out a model utility F test at a 0.05 significance level.State the null and alternative hypotheses.|OH: B₁ = B₂ =B₂ = 01.802.702.002.603.151.801.503.805.004.752.802.102.202.602.602.905.1010.203.501.201.701.751.701.201.207.504.25Elongation Volume1.501.071.981.79Calculate the test statistic. (Round your answer to two decimal places.)F=1.252.173.191.090.290.591.881.981.942.502.411.770.850.842.363.061.623.30(b) Why should we consider adjusted R² instead of R² when evaluating this model?Ⓒ We should consider the adjusted ² instead ofO We should consider the adjusted instead ofO We should consider the adjusted instead ofO We should consider the adjusted instead of2.802.833.171.301.62122133178Use technology to calculate the P-value. (Round your answer to four decimal places.)P-value =10 WN28832793118518333"NHW3401712442403653086301255(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 maximum width and x, for the elongation score.)65430632030824620512042327because it takes into account the number of predictors used in the model. In this case the adjusted 2 is noticeably less than ².because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably greater than ².728because it does not take 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 ² is noticeably greater than

Multiple regression analysis is also used to predict the variable based on two or more independent…

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 ŷ 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 tin tin 7.7 6.2 8.5 glass glass glass glass cardboard 8.7 cardboard 17.1 glass 16.5 glass glass glass glass glass plastic 10.4 8.0 8.7 10.2 10.5 3.4 6.9 10.9 OH:A₁-A₂-B₁ = 0 9.7 10.1 ⒸH₂: A₁ = ₂ = ₂ = 0 13.0 13.0 11.0 16.5 9.7 17.8 14.0 13.6 27.9 19.5 13.8 Maximum Minimum Width Width 2.50 2.90 H: BB, and , are all not 0 12 OHBB, and S, are all not 0 2.15 OH: at least one of ₁₂ or is not 0 H₂: A₁-B₂=₂=0 2.90 3.20 H: at least one of ₁.₂ or P₂ is not 0 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 (c) Carry out a model utility F test at a 0.05 significance level. State the null and alternative hypotheses. 4.25 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 (b) Why should we consider adjusted R² instead of R² when evaluating this model? We should consider the adjusted We should consider the adjusted O We should consider the adjusted O We should consider the adjusted 2. instead of instead of instead of instead of 2.80 2.83 3.17 1.30 1.62 122 133 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= 178 288 327 93 118 518 333 574 340 171 244 240 365 309 630 (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 maximum width and x, for the elongation score.) 1255 654 306 320 308 246 205 1204 2327 728 because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably less than. 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. because it does not take into account the number of predictors used in the model. In this case the adjusted is noticeably greater than