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

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


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


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



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 7-13 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 7-19 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


Minimize: C16





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


Solve for Annual Return


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 8-22 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





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


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


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.


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


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.


Sample graduation rate prediction

d.


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.

Documents

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