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North Group/Quiz 3

North Group/Quiz 3. Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal Deyanira Pena Professor Lawrence MIS 680. Table of Content. Ragsdale Book Deyanira Pena, 7-8, 8-22 Rosele Lynn, 7-13, 8-12

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North Group/Quiz 3

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  1. North Group/Quiz 3 Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal Deyanira Pena Professor Lawrence MIS 680

  2. Table of Content Ragsdale Book • Deyanira Pena, 7-8, 8-22 • Rosele Lynn, 7-13, 8-12 • Jose Lopez, 7-19, 8-4  Dielman's book • Dave Neal, 6-2 • Thamer AbuDiak, 7-2. • Reynald Benoit, 8-1

  3. Ragsdale 7-8 by Deyanira Pena Min: Q Subject to: 12x1 + 4x2 >= 48 } High-grade coal required 4x1 + 4x2 >= 28 } Medium-grade coal required 10x1 + 20x 2 >= } Low-grade coal required W1((40x1+32x2)-244)/244) <= Q } goal 1 MINIMAX constraint W2((800x1+1250x2-6950)/6950)<= Q } goal 2 MINIMAX constraint W3((.20x1+.45x2-2)/2) <= Q } goal 3 MINIMAX constraint X1x2 >= 0 } nonegativity conditions W1,w2,w3 are positive constraints

  4. Ragsdale 7-8 by Deyanira Pena

  5. Ragsdale 7-8 by Deyanira Pena

  6. Ragsdale 7-8 by Deyanira Pena

  7. Ragsdale 7-13 by Rosele Lynn Decision variables: Which combination of coal should be used? X1= coal type 1 X2= coal type 2 X3= coal type 3 Problem: Which combination of three types of coal should be used in order to maintain the EPA’s requirements for sulfur and coal dust levels?

  8. Ragsdale 7-13 by Rosele Lynn Objective Functions: MAX: 24,000X1 + 36,000X2 + 28,000X3 } maximize steam produced MIN: 1,100X1 + 3,500X2 + 1,300X3 } minimize sulfur emissions MIN: 1.7X1 + 3.2X2 + 2.4X3 } minimize coal dust emissions Constraints: X1 + X2 > 0 } non-negativity constraint X1+ X2 + X3/3 < 2,500 } for each ton of coal burned less than 2,500 ppm sulfur X1+ X2 + X3/3 < 2.8 } for each ton of coal burned less than 2.8 kg coal dust

  9. Ragsdale 7-13 by Rosele Lynn

  10. Ragsdale 7-13 by Rosele Lynn

  11. Ragsdale 7-13 by Rosele Lynn

  12. Ragsdale 7-13 by Rosele Lynn

  13. Ragsdale 7-19 by Jose F. Lopez (A & B) CONTRAINTS Subject to: 11X1>= 0 10X4 >= 0 8X2>= 0 9X5 >= 0 8.5X3>= 0 11X1+8X2+8.5X3+10X4…. +9X5 = 1 OBJECTIVES Maximize: 11X1 + 8X2 + 8.5X3 + 10X4 + 9X5 Average Yield on Funds Minimize: 8X1 + 1X2 + 7X3 + 6X4 + 2X5 Weighted Average Maturity Minimize: 5X1 + 2X2 + 1X3 + 5X4 + 3X5 Weighted Average Risk

  14. Ragsdale 7-19 by Jose F. Lopez (A & B) Minimize: C16 By Changing: B5:B9, C16 Subject To: C14: D14 <= C16 B10 = 1 B5:B9 >= 0

  15. Ragsdale 7-19 by Jose F. Lopez (A & B) Minimize: C16 By Changing: B5:B9, C16 Subject To: C14: D14 <= C16 B10 = 1 B5:B9 >= 0

  16. Ragsdale 8-12 by Rosele Lynn How does Pearman get the minimum amount of money to invest in order to have his after tax earnings cover his planned premium payments? Problem: How does Thom Pearman increase his life insurance coverage while keeping $6,000 in case of emergency?

  17. Ragsdale 8-12 by Rosele LynnSpreadsheet before Solver

  18. Ragsdale 8-12 by Rosele LynnSolve for Annual Return

  19. Ragsdale 8-12 by Rosele LynnMinimum Investment with 15% Annual Rate

  20. Ragsdale 8-12 by Rosele Lynn b. Solver tells us that this is a non linear model.

  21. Ragsdale 8-22 by Deyanira Pena X1= location of new plant with respect to the x-axis Y1=location of new plant with respect to the y-axis Min:  (9-x1)^2 + (45-y1)^2) + (2-x1)^2 + (28-y1)^2 + (51-x1)^2 + (36-y1)^2 + (19-X1)^2 + (4-Y1)^2 Subject to: (9-x1)^2 + (45-y1)^2 } Dalton distance constraint (2-x1)^2 + (28-y1)^2 }Rome distance constraint (51-x1)^2 + (36-y1)^2 }Canton distance constraint (19-X1)^2 + (4-Y1)^2 }Kennesaw distance constraint

  22. Ragsdale 8-22 by Deyanira Pena Minimize: C16 By Changing: B5:B9, C16 Subject To: C14: D14 <= C16 B10 = 1 B5:B9 >= 0

  23. Ragsdale 8-22 by Deyanira Pena

  24. Dielman 6-2 Dave NealRESEARCH AND DEVELOPMENT A company is interested in the relationship between profit (PROFIT) on a number of projects and 2 explanatory variables. These variables are the expenditure on research and development (RD) and a measure of risk assigned at the outset of the project (RISK). PROFIT is measured in thousands of dollars and RD is measured in hundreds of dollars.

  25. Dielman 6-2 Dave NealRESEARCH AND DEVELOPMENT (cont.) • Using any of the given outputs, does the linearity assumption appear to be violated? Justify your answer. • PROFIT vs. RD appears to be linear. R2 is 95.6%. • PROFIT vs. RD and RISK appears to be linear. R2 is 99.2%. • PROFIT vs. RISK appears to violate the linearity assumption. R2 is only 50.6%. • If you answered yes, state how the violation might be corrected. • PROFIT vs. RISK can be corrected by trying a quadratic and cubic polynomial regression analysis to see if the R2 value is improved. • Then try your correction using a computer regression routine. • See the attached quadratic and cubic polynomial regression analysis data and plots. • Does your model appear to be an improvement over the original model? Justify your answer. • Yes, the quadratic and cubic polynomial regression analysis appears to be an improvement over the original model. R2 improved from 50.6% to 71.0% within a 95% Confidence Interval.

  26. Dielman 6-2 Dave NealRESEARCH AND DEVELOPMENT (cont.) Regression Analysis: PROFIT versus RD The regression equation is PROFIT = - 295 + 5.21 RD Predictor Coef SE Coef T P Constant -294.84 28.05 -10.51 0.000 RD 5.2079 0.2808 18.54 0.000 S = 31.8337 R-Sq = 95.6% R-Sq(adj) = 95.3% Analysis of Variance Source DF SS MS F P Regression 1 348510 348510 343.91 0.000 Residual Error 16 16214 1013 Total 17 364724 ____________________________________________________________ Regression Analysis: PROFIT versus RISK The regression equation is PROFIT = - 490 + 90.5 RISK Predictor Coef SE Coef T P Constant -489.5 173.6 -2.82 0.012 RISK 90.45 22.33 4.05 0.001 S = 106.087 R-Sq = 50.6% R-Sq(adj) = 47.5% Analysis of Variance Source DF SS MS F P Regression 1 184652 184652 16.41 0.001 Residual Error 16 180072 11255 Total 17 364724

  27. Dielman 6-2 Dave NealRESEARCH AND DEVELOPMENT (cont.) Regression Analysis: PROFIT versus RD, RISK The regression equation is PROFIT = - 453 + 4.51 RD + 29.3 RISK Predictor Coef SE Coef T P Constant -453.18 23.51 -19.28 0.000 RD 4.5100 0.1538 29.33 0.000 RISK 29.309 3.669 7.99 0.000 S = 14.3420 R-Sq = 99.2% R-Sq(adj) = 99.0% Analysis of Variance Source DF SS MS F P Regression 2 361639 180820 879.08 0.000 Residual Error 15 3085 206 Total 17 364724 Source DF Seq SS RD 1 348510 RISK 1 13129 Unusual Observations Obs RD PROFIT Fit SE Fit Residual St Resid 9 152 536.00 508.94 7.98 27.06 2.27R R denotes an observation with a large standardized residual.

  28. Dielman 6-2 Dave NealRESEARCH AND DEVELOPMENT (cont.)

  29. Dielman 6-2 Dave NealRESEARCH AND DEVELOPMENT (cont.)

  30. Dielman 7-2 Thamer AbuDiakGraduation Rate • Variables: • y: Percentage of students who earned a bachelor degree in 4 years (GRADRATE4) • x1: Admission Rate expressed as a percentage (ADMINRATE) • x2: indicator variable coded as 1 for private and 0 for public school. • The regression equation is: • y = 0.589 - 0.350 x1 + 0.282 x2

  31. Dielman 7-2 Thamer AbuDiakGraduation Rate • F-test: • F = (SSER – SSEF)/(K-L)MSEF = (7.1215- 3.75) / (2*.0195) = 86.44 • Decision rule: • H0 if F > 3.49 • Do not reject H0 if F <= 3.49 • Since 86 > 3.49, the null hypotheses is rejected. • There are difference in the graduation rate between public and private schools.

  32. Dielman 7-2 Thamer AbuDiakGraduation Rate • Difference in graduation rates between public and private schools. • Public school: y = 0.636 - 0.421 x1 • Private school y = 0.852 - 0.305 x1 • Private schools have a higher graduation rate than public schools.

  33. Dielman 7-2 Thamer AbuDiakGraduation Rate d. Sample graduation rate prediction

  34. Dielman 7-2 Thamer AbuDiakGraduation Rate Regression without counting x2 as a factor Regression with counting x2 as a factor

  35. Dielman 8-1 Reynald BenoitBackward elimination. Alpha-to-Remove: 0.1Response is COST on 4 predictors, with N = 27 S 11.1 10.8 11.0 R-Sq 99.88 99.88 99.87 R-Sq(adj) 99.86 99.87 99.86 Mallows C-p 5.0 3.0 2.6

  36. Dielman 8-1 Reynald Benoit-cont • A) What is the equation? • COST = 59.43 + 0.95PAPER + 2.39MACHINE • B) What is the R2? • 99.87% • C) What is the Adjusted R2? • 99.86% • D) What is the standard error? • 11.0 • E) What variables were omitted? Are they related to cost? • Overhead and Labor. They are related to cost but paper and machine explains 99% of the variation in cost.

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