North Group/Quiz 3 Thamer AbuDiak Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal...
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Transcript of North Group/Quiz 3 Thamer AbuDiak Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal...
North Group/Quiz 3North Group/Quiz 3
Thamer AbuDiakThamer AbuDiak
Reynald BenoitReynald BenoitJose LopezJose Lopez
Rosele LynnRosele LynnDave NealDave Neal
Deyanira PenaDeyanira Pena
Professor LawrenceProfessor LawrenceMIS 680MIS 680
Table of ContentTable of Content
Ragsdale BookRagsdale Book Deyanira Pena, 7-8, 8-22 Deyanira Pena, 7-8, 8-22 Rosele Lynn, 7-13, 8-12Rosele Lynn, 7-13, 8-12 Jose Lopez, 7-19, 8-4Jose Lopez, 7-19, 8-4 Dielman's bookDielman's book Dave Neal, 6-2 Dave Neal, 6-2 Thamer AbuDiak, 7-2.Thamer AbuDiak, 7-2. Reynald Benoit, 8-1Reynald Benoit, 8-1
Ragsdale 7-8 by Deyanira PenaRagsdale 7-8 by Deyanira Pena
Min: QSubject to:12x1 + 4x2 >= 48 } High-grade coal required4x1 + 4x2 >= 28 } Medium-grade coal required10x1 + 20x 2 >= } Low-grade coal required W1((40x1+32x2)-244)/244) <= Q } goal 1 MINIMAX constraintW2((800x1+1250x2-6950)/6950)<= Q } goal 2 MINIMAX constraintW3((.20x1+.45x2-2)/2) <= Q } goal 3 MINIMAX constraintX1x2 >= 0 } nonegativity conditionsW1,w2,w3 are positive constraints
Ragsdale 7-8 by Deyanira PenaRagsdale 7-8 by Deyanira Pena
Blackstone Minning Co.
Wythe GilesMonths to operate 0
Weighted %Objectives Total Target Value %Deviation Weight DeviationCost per month $40 $32 0 $244.00 -100% 1 -100%Toxins per month 800 1250 0 6950 -100% 1 -100%Accidents per month 0.2 0.45 0 2 -100% 1 -100%
Constraints Available RequiredHG coal produced 12 4 0 48MG coal produced 4 4 0 28LG coal produced 10 20 0 100
Objective MiniMax Variable
Blackstone Minning Co.
Wythe GilesMonths to operate 4.23 2.88
Weighted %Objectives Total Target Value %Deviation Weight DeviationCost per month $40 $32 261.590 $244.0 7.21% 1 7.21%Toxins per month 800 1,250 6990.758 $6,950.0 0.59% 1 0.59%Accidents per month 0.2 0.45 2.144 $2.0 7.21% 1 7.21%
Constraints Available RequiredHG coal produced 12 4 62.33 48MG coal produced 4 4 28.47 28LG coal produced 10 20 100 100
Objective MiniMax Variable 0.072088725
Ragsdale 7-8 by Deyanira PenaRagsdale 7-8 by Deyanira Pena
Blackstone Minning Co.
Wythe GilesMonths to operate 4.00 3.00
Weighted %Objectives Total Target Value %Deviation Weight DeviationCost per month $40 $32 256 $244.0 4.92% 1 4.92%Toxins per month 800 1,250 6950 $6,950.0 0.00% 1 0.00%Accidents per month 0.2 0.45 2.15 $2.0 7.50% 1 7.50%
Constraints Available RequiredHG coal produced 12 4 60 48MG coal produced 4 4 28 28LG coal produced 10 20 100 100
Objective MiniMax Variable 0.075
Ragsdale 7-8 by Deyanira PenaRagsdale 7-8 by Deyanira Pena
Ragsdale 7-13 by Ragsdale 7-13 by Rosele LynnRosele Lynn
Problem: Which combination of three types of coal Problem: Which combination of three types of coal should be used in order to maintain the EPA’s should be used in order to maintain the EPA’s requirements for sulfur and coal dust levels?requirements for sulfur and coal dust levels?
Decision variables: Which combination of coal should be used?
X1= coal type 1
X2= coal type 2
X3= coal type 3
Objective Functions:Objective Functions:
MAX: 24,000X1 + 36,000X2 + 28,000X3 } maximize steam producedMAX: 24,000X1 + 36,000X2 + 28,000X3 } maximize steam produced
MIN: 1,100X1 + 3,500X2 + 1,300X3 } minimize sulfur emissionsMIN: 1,100X1 + 3,500X2 + 1,300X3 } minimize sulfur emissions
MIN: 1.7X1 + 3.2X2 + 2.4X3 } minimize coal dust emissionsMIN: 1.7X1 + 3.2X2 + 2.4X3 } minimize coal dust emissions
Constraints:
X1 + X2 > 0 } non-negativity constraintX1+ X2 + X3/3 < 2,500 } for each ton of coal burned less than 2,500 ppm sulfurX1+ X2 + X3/3 < 2.8 } for each ton of coal burned less than 2.8 kg coal dust
Ragsdale 7-13 by Rosele LynnRagsdale 7-13 by Rosele Lynn
Ragsdale 7-13 by Rosele LynnRagsdale 7-13 by Rosele Lynn
Ragsdale 7-13 by Rosele LynnRagsdale 7-13 by Rosele Lynn
Ragsdale 7-13 by Rosele LynnRagsdale 7-13 by Rosele Lynn
Ragsdale 7-13 by Rosele LynnRagsdale 7-13 by Rosele Lynn
Ragsdale 7-19 by Jose F. Lopez (A & B)Ragsdale 7-19 by Jose F. Lopez (A & B)
OBJECTIVESMaximize: 11X1 + 8X2 + 8.5X3 + 10X4 + 9X5 Average Yield on FundsMinimize: 8X1 + 1X2 + 7X3 + 6X4 + 2X5 Weighted Average MaturityMinimize: 5X1 + 2X2 + 1X3 + 5X4 + 3X5 Weighted Average Risk
CONTRAINTSSubject to: 11X1 >= 0 10X4 >= 0 8X2 >= 0 9X5 >= 08.5X3 >= 011X1+8X2+8.5X3+10X4….+9X5 = 1
Minimize: C16
By Changing: B5:B9, C16
Subject To:C14: D14 <= C16B10 = 1B5:B9 >= 0
Ragsdale 7-19 by Jose F. Lopez (A & B)Ragsdale 7-19 by Jose F. Lopez (A & B)
Minimize: C16
By Changing: B5:B9, C16
Subject To:C14: D14 <= C16B10 = 1B5:B9 >= 0
Ragsdale 7-19 by Jose F. Lopez (A & B)Ragsdale 7-19 by Jose F. Lopez (A & B)
Ragsdale 8-12 by Rosele LynnRagsdale 8-12 by Rosele Lynn
Problem: How does Thom Pearman increase his life Problem: How does Thom Pearman increase his life insurance coverage while keeping $6,000 in case of insurance coverage while keeping $6,000 in case of emergency?emergency?
How does Pearman get the minimum amount of money to invest in order to have his after tax earnings cover his planned premium
payments?
Ragsdale 8-12 by Rosele LynnRagsdale 8-12 by Rosele LynnSpreadsheet before Solver
Ragsdale 8-12 by Rosele LynnRagsdale 8-12 by Rosele Lynn
Solve for Annual Return
Ragsdale 8-12 by Rosele LynnRagsdale 8-12 by Rosele Lynn
Minimum Investment with 15% Annual Rate
b. Solver tells us that this is a non linear b. Solver tells us that this is a non linear model.model.
Ragsdale 8-12 by Rosele LynnRagsdale 8-12 by Rosele Lynn
Ragsdale 8-22 by Deyanira Ragsdale 8-22 by Deyanira PenaPena
X1= location of new plant with respect to the x-axisX1= location of new plant with respect to the x-axis
Y1=location of new plant with respect to the y-axisY1=location of new plant with respect to the y-axis
Min: Min:
(9-x1)^2 + (45-y1)^2) + (9-x1)^2 + (45-y1)^2) + (2-x1)^2 + (28-y1)^2 + (2-x1)^2 + (28-y1)^2 + (51-x1)^2 + (36-y1)^2 (51-x1)^2 + (36-y1)^2 + + (19-X1)^2 + (4-Y1)^2(19-X1)^2 + (4-Y1)^2
Subject to:Subject to:
(9-x1)^2 + (45-y1)^2 } Dalton distance constraint(9-x1)^2 + (45-y1)^2 } Dalton distance constraint
(2-x1)^2 + (28-y1)^2 (2-x1)^2 + (28-y1)^2 }Rome distance constraint}Rome distance constraint
(51-x1)^2 + (36-y1)^2 (51-x1)^2 + (36-y1)^2 }Canton distance constraint}Canton distance constraint
(19-X1)^2 + (4-Y1)^2(19-X1)^2 + (4-Y1)^2 }Kennesaw distance constraint}Kennesaw distance constraint
Minimize: C16
By Changing: B5:B9, C16
Subject To:C14: D14 <= C16B10 = 1B5:B9 >= 0
Ragsdale 8-22 by Deyanira Ragsdale 8-22 by Deyanira PenaPena
Ragsdale 8-22 by Deyanira Ragsdale 8-22 by Deyanira PenaPena
Rugger Corporation Rugger Corporation
CoordinatesCoordinates
xx yy Distance Distance Maximum Maximum
PlantPlant 12.4103512.41035 29.6996329.69963 to Plantto Plant AllowedAllowed
DaltonDalton 99 4343 13.7306308813.73063088 130130
RomeRome 22 2828 10.5481773810.54817738 7575
CantonCanton 5151 3636 39.1005889739.10058897 9090
KennesawKennesaw 1919 44 26.531013426.5310134 8080
Total Total 89.9104106389.91041063
Dielman 6-2 Dave NealDielman 6-2 Dave NealRESEARCH AND DEVELOPMENTRESEARCH AND DEVELOPMENT
A company is interested in the relationship A company is interested in the relationship between profit (PROFIT) on a number of between profit (PROFIT) on a number of projects and 2 explanatory variables.projects and 2 explanatory variables.These variables are the expenditure on These variables are the expenditure on research and development (RD) and a research and development (RD) and a measure of risk assigned at the outset of measure of risk assigned at the outset of the project (RISK).the project (RISK).PROFIT is measured in thousands of PROFIT is measured in thousands of dollars and RD is measured in hundreds of dollars and RD is measured in hundreds of dollars.dollars.
Dielman 6-2 Dave NealDielman 6-2 Dave Neal RESEARCH AND DEVELOPMENTRESEARCH AND DEVELOPMENT (cont.) (cont.)
1.1. Using any of the given outputs, does the linearity assumption Using any of the given outputs, does the linearity assumption appear to be violated? Justify your answer.appear to be violated? Justify your answer.
PROFIT vs. RD appears to be linear. RPROFIT vs. RD appears to be linear. R22 is 95.6%. is 95.6%. PROFIT vs. RD and RISK appears to be linear. RPROFIT vs. RD and RISK appears to be linear. R22 is 99.2%. is 99.2%. PROFIT vs. RISK appears to violate the linearity assumption. RPROFIT vs. RISK appears to violate the linearity assumption. R22 is is
only 50.6%.only 50.6%.2.2. If you answered yes, state how the violation might be corrected.If you answered yes, state how the violation might be corrected.
PROFIT vs. RISK can be corrected by trying a quadratic and cubic PROFIT vs. RISK can be corrected by trying a quadratic and cubic polynomial regression analysis to see if the Rpolynomial regression analysis to see if the R22 value is improved. value is improved.
3.3. Then try your correction using a computer regression routine.Then try your correction using a computer regression routine. See the attached quadratic and cubic polynomial regression analysis See the attached quadratic and cubic polynomial regression analysis
data and plots. data and plots. 4.4. Does your model appear to be an improvement over the original Does your model appear to be an improvement over the original
model? Justify your answer.model? Justify your answer. Yes, the quadratic and cubic polynomial regression analysis appears Yes, the quadratic and cubic polynomial regression analysis appears
to be an improvement over the original model. Rto be an improvement over the original model. R22 improved from improved from 50.6% to 71.0% within a 95% Confidence Interval.50.6% to 71.0% within a 95% Confidence Interval.
Dielman 6-2 Dave NealDielman 6-2 Dave Neal RESEARCH AND DEVELOPMENTRESEARCH AND DEVELOPMENT (cont.) (cont.)Regression Analysis: PROFIT versus RDRegression Analysis: PROFIT versus RD The regression equation isThe regression equation isPROFIT = - 295 + 5.21 RDPROFIT = - 295 + 5.21 RD
Predictor Coef SE Coef T PPredictor Coef SE Coef T PConstant -294.84 28.05 -10.51 0.000Constant -294.84 28.05 -10.51 0.000RD 5.2079 0.2808 18.54 0.000RD 5.2079 0.2808 18.54 0.000
S = 31.8337 S = 31.8337 R-Sq = 95.6%R-Sq = 95.6% R-Sq(adj) = 95.3% R-Sq(adj) = 95.3%
Analysis of VarianceAnalysis of VarianceSource DF SS MS F PSource DF SS MS F PRegression 1 348510 348510 343.91 0.000Regression 1 348510 348510 343.91 0.000Residual Error 16 16214 1013Residual Error 16 16214 1013Total 17 364724Total 17 364724________________________________________________________________________________________________________________________
Regression Analysis: PROFIT versus RISK Regression Analysis: PROFIT versus RISK The regression equation isThe regression equation isPROFIT = - 490 + 90.5 RISKPROFIT = - 490 + 90.5 RISK
Predictor Coef SE Coef T PPredictor Coef SE Coef T PConstant -489.5 173.6 -2.82 0.012Constant -489.5 173.6 -2.82 0.012RISK 90.45 22.33 4.05 0.001RISK 90.45 22.33 4.05 0.001
S = 106.087 S = 106.087 R-Sq = 50.6%R-Sq = 50.6% R-Sq(adj) = 47.5% R-Sq(adj) = 47.5%
Analysis of VarianceAnalysis of VarianceSource DF SS MS F PSource DF SS MS F PRegression 1 184652 184652 16.41 0.001Regression 1 184652 184652 16.41 0.001Residual Error 16 180072 11255Residual Error 16 180072 11255Total 17 364724Total 17 364724
Dielman 6-2 Dave NealDielman 6-2 Dave Neal RESEARCH AND DEVELOPMENTRESEARCH AND DEVELOPMENT (cont.) (cont.)Regression Analysis: PROFIT versus RD, RISKRegression Analysis: PROFIT versus RD, RISK The regression equation isThe regression equation isPROFIT = - 453 + 4.51 RD + 29.3 RISKPROFIT = - 453 + 4.51 RD + 29.3 RISK
Predictor Coef SE Coef T PPredictor Coef SE Coef T PConstant -453.18 23.51 -19.28 0.000Constant -453.18 23.51 -19.28 0.000RD 4.5100 0.1538 29.33 0.000RD 4.5100 0.1538 29.33 0.000RISK 29.309 3.669 7.99 0.000RISK 29.309 3.669 7.99 0.000
S = 14.3420 S = 14.3420 R-Sq = 99.2%R-Sq = 99.2% R-Sq(adj) = 99.0% R-Sq(adj) = 99.0%
Analysis of VarianceAnalysis of VarianceSource DF SS MS F PSource DF SS MS F PRegression 2 361639 180820 879.08 0.000Regression 2 361639 180820 879.08 0.000Residual Error 15 3085 206Residual Error 15 3085 206Total 17 364724Total 17 364724
Source DF Seq SSSource DF Seq SSRD 1 348510RD 1 348510RISK 1 13129RISK 1 13129
Unusual ObservationsUnusual Observations
Obs RD PROFIT Fit SE Fit Residual St ResidObs RD PROFIT Fit SE Fit Residual St Resid 9 152 536.00 508.94 7.98 27.06 2.27R9 152 536.00 508.94 7.98 27.06 2.27RR denotes an observation with a large standardized residual.R denotes an observation with a large standardized residual.
Dielman 6-2 Dave NealDielman 6-2 Dave Neal RESEARCH AND DEVELOPMENTRESEARCH AND DEVELOPMENT (cont.) (cont.)
RDPROFI
T1501251007550
600
500
400
300
200
100
0
Scatterplot of PROFIT vs RD
RISK
PROFI
T
1098765
600
500
400
300
200
100
0
Scatterplot of PROFIT vs RISK
Dielman 6-2 Dave NealDielman 6-2 Dave Neal RESEARCH AND DEVELOPMENTRESEARCH AND DEVELOPMENT (cont.) (cont.)
RISK
PROFI
T
1098765
700
600
500
400
300
200
100
0
S 84.0651R-Sq 70.9%R-Sq(adj) 67.1%
Regression95% CI
Fitted Line PlotPROFIT = 1830 - 519.6 RISK
+ 39.27 RISK**2
RISKPROFI
T1098765
800
700
600
500
400
300
200
100
0
S 86.9713R-Sq 71.0%R-Sq(adj) 64.7%
Regression95% CI
Fitted Line PlotPROFIT = 2388 - 744 RISK
+ 68.9 RISK**2 - 1.28 RISK**3
Dielman 7-2 Thamer AbuDiakDielman 7-2 Thamer AbuDiakGraduation RateGraduation Rate Variables:Variables:
y: Percentage of students who earned a y: Percentage of students who earned a bachelor degree in 4 years (GRADRATE4)bachelor degree in 4 years (GRADRATE4)
xx11: Admission Rate expressed as a : Admission Rate expressed as a
percentage (ADMINRATE)percentage (ADMINRATE) xx22: indicator variable coded as 1 for private : indicator variable coded as 1 for private
and 0 for public school.and 0 for public school.
The regression equation is:The regression equation is: y = 0.589 - 0.350 xy = 0.589 - 0.350 x11 + 0.282 x + 0.282 x22
Dielman 7-2 Thamer AbuDiakDielman 7-2 Thamer AbuDiakGraduation RateGraduation Ratea.a. F-test:F-test:
i.i. F = (SSEF = (SSERR – SSE – SSEFF)/(K-L)MSE)/(K-L)MSEFF = (7.1215- 3.75) / = (7.1215- 3.75) /
(2*.0195) = 86.44(2*.0195) = 86.44
ii.ii. Decision rule:Decision rule:i.i. H0 if F > 3.49H0 if F > 3.49
ii.ii. Do not reject H0 if F <= 3.49Do not reject H0 if F <= 3.49
iii.iii. Since 86 > 3.49, the null hypotheses is rejected.Since 86 > 3.49, the null hypotheses is rejected.
b.b. There are difference in the graduation rate There are difference in the graduation rate between public and private schools.between public and private schools.
Dielman 7-2 Thamer AbuDiakDielman 7-2 Thamer AbuDiakGraduation RateGraduation Rate
c.c. Difference in graduation rates between Difference in graduation rates between public and private schools.public and private schools.
• Public school: y = 0.636 - 0.421 xPublic school: y = 0.636 - 0.421 x11
• Private school y = 0.852 - 0.305 xPrivate school y = 0.852 - 0.305 x11
• Private schools have a higher graduation Private schools have a higher graduation rate than public schools.rate than public schools.
Dielman 7-2 Thamer AbuDiakDielman 7-2 Thamer AbuDiakGraduation RateGraduation Rate
Sample graduation rate prediction
d.
Dielman 7-2 Thamer AbuDiakDielman 7-2 Thamer AbuDiakGraduation RateGraduation Rate
Regression without counting x2 as a factor
Regression with counting x2 as a factor
S 11.1 10.8 11.0R-Sq 99.88 99.88 99.87R-Sq(adj) 99.86 99.87 99.86Mallows C-p 5.0 3.0 2.6
StepStep
ConstantConstant
11
51.7251.72
22
51.1751.17
33
59.4359.43
PaperPaper
T-valueT-value
P-valueP-value
0.950.95
7.907.90
0.000.00
0.940.94
8.698.69
0.000.00
0.950.95
8.628.62
0.000.00
MachineMachine
T-valueT-value
P-valueP-value
2.472.47
5.315.31
0.000.00
2.512.51
11.0111.01
0.000.00
2.392.39
11.3611.36
0.000.00
OverheadOverhead
T-valueT-value
P-valueP-value
0.050.05
0.090.09
0.9270.927
LaborLabor
T-valueT-value
P-valueP-value
-0.051-0.051
-1.26-1.26
0.2230.223
-0.051-0.051
-1.29-1.29
0.2100.210
Dielman 8-1 Reynald BenoitDielman 8-1 Reynald Benoit
Backward elimination. Alpha-to-Remove: 0.1Backward elimination. Alpha-to-Remove: 0.1
Response is COST on 4 predictors, with N = 27Response is COST on 4 predictors, with N = 27
Dielman 8-1 Reynald BenoitDielman 8-1 Reynald Benoit-cont-cont
A) What is the equation? A) What is the equation? COST = 59.43 + 0.95PAPER + 2.39MACHINECOST = 59.43 + 0.95PAPER + 2.39MACHINE
B) What is the R2? B) What is the R2? 99.87%99.87%
C) What is the Adjusted R2? C) What is the Adjusted R2? 99.86%99.86%
D) What is the standard error? D) What is the standard error? 11.011.0
E) What variables were omitted? Are they related to cost? E) What variables were omitted? Are they related to cost? Overhead and Labor. They are related to cost but paper and Overhead and Labor. They are related to cost but paper and
machine explains 99% of the variation in cost. machine explains 99% of the variation in cost.