EMIS/STAT 4/5/7377 Final Exam 2020InstructionsThe exam is an open book take-home exam that runs for 3 hours. Clearly indicate all the assumptions you make and show all the steps of your work to qualify for partial credits.Important:Please write the final exam inone sitting – you are not allowed to work on the exam intermittentlyReturn the completed exam via email or upload via Canvas.Return the completed examno later than May 12 by 1100am CST.Take the examindividually – no collaboration is allowedNote: If you need to scan handwritten pages, please consider using an app on your phone: either Evernote Scannable, Microsoft Office Lens, or ScanBot. Use the app to combine scanned pages into a PDF and email me the file.Important: read, sign, and date the following before writing the exam and ensure the signed pledge is included in your exam submission.HONOR PLEDGEOn my honor, I have neither given nor received unauthorized aid on this exam.SIGNED__________________________DATE____________________________Problem 1 [40 points]. The horsepower developed by an automobile engine on a dynamometer is thought to be a function of the engine speed in revolutions per minute (rpm), the road octane number of the fuel, and the engine compression. An experiment is run in the laboratory and the following data are collected. Factor 1 Factor 2 Factor 3 Response Engine speed [rpm] Fuel type [octane number] Engine compression [psi] Dynamometer [horsepower] 2000 90 100 225 1800 94 95 212 2400 88 110 229 1900 91 96 222 1600 86 100 219 2500 96 110 278 3000 94 98 246 3200 90 100 237 2800 88 105 233 3400 86 97 224 1800 90 100 223 2500 89 104 230 1. [10pt] Fit a multiple linear regression model to the data.2. [10pt] Test the regression significance3. [10pt] Evaluate the residuals and comment on model accuracy4. [10pt] Redo the analysis by adding interaction terms to the modelProblem 2 [20 points]Consider the three-variable central composite design shown in the following table with 3 factors and two responses – conversion % and quantity. Analyze the data and draw appropriate conclusions, assuming that we wish to maximize conversion (y1) with quantity (y2) between 55 and 60 . Run Time [min] Temperature [oC] Catalyst [%] Conversion [%] Activity [qty] A B C y1 y2 1 -1 -1 -1 74 53.2 2 1 -1 -1 51 62.9 3 -1 1 -1 88 53.4 4 1 1 -1 70 62.6 5 -1 -1 1 71 57.3 6 1 -1 1 90 67.9 7 -1 1 1 66 59.8 8 1 1 1 97 67.8 9 0 0 0 81 59.2 10 0 0 0 75 60.4 11 0 0 0 76 59.1 12 0 0 0 83 60.6 13 -1.682 0 0 76 59.1 14 1.682 0 0 79 65.9 15 0 -1.682 0 85 60 16 0 1.682 0 97 60.7 17 0 0 -1.682 55 57.4 18 0 0 1.682 81 63.2 19 0 0 0 80 60.8 20 0 0 0 91 58.9 1. [5pts] Develop quadratic models for Conversion and Quantity including quadratic and two factor interactions.2. [5pts] Reduce the quadratic model by eliminating insignificant terms as appropriate3. [5pts] Sketch a contour plot for Conversion and Quantity respectively 4. [5pts] Sketch the overlay plot Problem 3 [30 points]A chemical engineer collected the following empirical process operation data. The response y is filtration time, while coded variable x1 is temperature, and x2 is pressure. A: Temperature B: Pressure R1: Filtration Time x1 x2 y -1 -1 54 -1 1 45 1 -1 32 1 1 47 -1.414 0 50 1.414 0 53 0 -1.414 47 0 1.414 51 0 0 41 0 0 39 0 0 44 0 0 42 0 0 40 1. [10pts] Fit a second order model including AB and A2 and evaluate the lack of fit.2. [10pts] Sketch a contour plot and identify the recommended operating conditions to minimize filtration time. Estimate the predicted filtration time under those conditions.3. [10pts] What operating conditions would you recommend if the objective is to operate the process at a mean filtration time very close to 46.Problem 4 [10 points – EMIS 7377 students only] A manufacturer of cutting tools has developed two empirical equations for tool life in hours (y1) and for tool cost in dollars (y2). Both models are linear functions of steel hardness (x1) and manufacturing time (x2). The two equations are:and both equations are valid over the range . Unit tool cost must be below $27.50 and expected tool life must exceed 12 hours for the product to be competitive. 1. [2.5pts] Sketch contour plots for the two models.2. [2.5pts] Sketch the overlay plot3. [2.5pts] Is there a feasible set of operating conditions for this process? 4. [2.5pts] Where would you recommend that the process be run?