(c) Carry out a model utility F test at a 0.05 significance level.State the null and alternative hypotheses.O Ho: P₂ = P₂ - Py = 0HPand are all not 0OHP₂ and A, are all not 0H₂: P₂ P₂P₂-0ⒸH₂i P₂ P₂ P₂ -0H: at least one of P₁, P₂ or Pg is not oOH.: at least one of A₂, B₂ or Ay is not oH₂: P₂P₂P₂-0Calculate 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=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 is not 0.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 ₁.₂ andO 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 P₂ P₂ or By is not 0.O Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁, ₂ and are all not 0. A statistical program is recommended.An article gave the data, shown in the table below, on dimensions of 27 representative food products.Product9-123456789101112131415161718192021222324252627Material Heightglassglassglassglassplasticglassglassplasticplasticplastictinplasticglassglassglassglassglassglassglass7.7tin6.2tin8.510.48.08.710.2glassglassglasscardboard 8.7cardboard10.53.46.910.99.710.113.013.011.017.116.516.59.717.814.0plastic 27.913.619.513.8Maximum MinimumWidthWidth2.502.902.152.903.202.001.604.805.905.802.902.452.602.602.703.105.1010.203.502.703.002.702.502.404.407.504.251.802.702.002.603.151.801.503.805.004.752.802.102.202.602.602.905.1010.203.501.201.701.751.701.201.207.504.25Elongation Volume1.501.071.981.791.252.173.191.090.290.591.881.981.942.502.411.770.850.842.363.061.623.302.802.833.171.301.62123(b) Why should we consider adjusted R2 instead of R2 when evaluating this model?We should consider the adjustedWe should consider the adjustedWe should consider the adjustedWe should consider the adjusted13317828332786116521325574335171240235360307639125564630831930024120512062332(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.)729instead of 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.instead of 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.instead ofbecause it takes into account the number of predictors used in the model. In this case the adjusted 2 is noticeably less than ².instead ofbecause it takes into account the number of predictors used in the model. In this case the adjusted is noticeably greater than ².

The response variable, volume is denoted by y; the predictor variables, minimum width, maximum…

A statistical program is recommended. An article gave the data, shown in the table below, on dimensions of 27 representative food products Product Material 1 2 3 S 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 8.5 10.4 8.0 8.7 10.2 plastic 10.5 3.4 6.9 plastic plastic tin plastic glass glass glass glass glass glass glass Height glass 7.7 glass cardboard 8.7 glass plastic cardboard 17.1 tin tin 10.9 9.7 10.1 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 2.15 2.90 3.20 2.00 1.60 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 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 3.17 1.30 1.62 123 (b) Why should we consider adjusted R² instead of R² when evaluating this model? We should consider the adjusted We should consider the adjusted We should consider the adjusted We should consider the adjusted instead of instead of instead of instead of 133 178 283 327 86 116 325 574 335 171 240 235 360 307 639 1255 308 319 300 241 205 1206 2332 729 (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.) 9- 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 does not take 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 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