2. We wish to analyze the monthly water usage of a production plant, Y (in gallons), withrespect to its monthly production X₁ (in tons), mean monthly temperature X₂ (in °F)and the monthly number of days X3 of plant operation using the data given in the file'WATER.xlsx'. The following models are considered:I:II:Y =Y =Bo + B₁X₁ + B₂X2 + ß3X3 + E,Bo + B₁X₁ + B2X2 + B3X3 + B₁X1X2 + B5X₁X3 + B6X2X3 + εPerform your tests at a = 10% in this question.(a) Generate a matrix scatter plot and state the relationship among these variables.(b) Use R/Minitab to estimate the parameters of Model I, set up three hypotheses to testwhether each variable is useful given that the other variables are in the model.(c) In Model II, the interaction terms among these three variables are considered. Usingthe sum of squared residuals from the estimates of models I and II, do an F-test totest the whether all these interaction terms are useful jointly in predicting the monthlywater usage of the production plant.1(d) Use backward selection to perform the model selection based on Model II as the fullmodel.i. State your selected model. Is it a good model for the prediction of monthly waterusage of the production plant? Explain your answer.ii. Use your model in 2(d)i to estimate the water usage of the plant during a monthwhen its production is 90.0 tons, the mean temperature is 65 °F, and it operatesfor 20 days. ABWater Production2228260930885237861980717178 27239 203110 190211 1721123+412225413 252214260915222816255917 272318 308819 252220 201221225422 24362324624214725237826203127171728 211729 190230 225131 235732172133198098.5108.2109.610183.370144.784.497.4131.882.164.51089711314410964918212611185101847010797989613284DDays67.41970.32082.12169.22164.5 1963.7 2158 192017231844.1 19702068Temperature58.136.649.644.366588244614459621999903aa132120182121541869215820642151 22361756 2285 1949 2364 19

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y , heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • x2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables S 1 {o if if advanced if aeroderivative and x4 X3 = not 0 if not Write a complete second-order model for heat rate (y ) as a function of cycle speed, cycle pressure ratio, and engine type.
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