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  • Level: GCSE
  • Subject: Maths
  • Word count: 2295

Applied Statistics

Extracts from this document...

Introduction

NAPIER UNIVERSITY

SCHOOL OF MATHEMATICS AND STATISTICS

MODULE MA32808

APPLIED STATISTICS

MULTIPLE REGRESSION COURSEWORK

Student: Nicolas LEGRAIS       07007619

Assessor: Phillip DARBY

Moderator: Dr Sandra BONELLIE


1/ In order to obtain an equation to predict the quality of the product, we used a model with all the variables.

Equation to predict the quality of the product, ignoring the variable shift:

Qualprod= -10,354+0,041*Temp1+0,002*Temp2+0,671*Recycle+0,620*Qualraw

This model has an R-Square value of 0,952 (95,2% of the variations are explained by the variables) but this equation isn’t the good one because with have too much variables with the high sig. (Appendix Q1)

Prediction of the mean quality of the product (with a 95% confidence interval) if the following settings were used:

a/ Temp1=200 Temp2=300 Recycle=4% Qualraw=15

Prediction of the mean quality: PRE_1=10,4458

Mean confidence interval: [LMCI_1 ; UNCI_1]=[6,6514 ; 14,2402]

b/ Temp1=200 Temp2=300 Recycle=14% Qualraw=15

Prediction of the mean quality: PRE_1=17,1519

Mean confidence interval: [LMCI_1 ; UNCI_1]=[6,2760 ; 28,0278]

  1. We saw in 1/ that we can’t accept the simple model because there were too much variables with a high sig. Thus we have used different approaches to variable selection in order to obtain the final equation.

We used Stepwise regression, Backward elimination and Forward selection. In each approach we can see that we obtained the same R-Square value of 0,952 but we also obtained a better equation than with the simple model. We can also see that in each approach the variable Temp2 has been dropped.

...read more.

Middle

,042

3

(Constant)

-9,726

2,796

-3,478

,002

Qualraw

,620

,088

,665

7,053

,000

Temp1

,041

,013

,278

3,100

,005

Recycle

,642

,210

,145

3,056

,005

a  Dependent Variable: Qualprod

        Variables Entered/Removed(b)

Model

Variables Entered

Variables Removed

Method

1

Qualraw, Temp2, Recycle, Temp1(a)

.

Enter

2

.

Temp2

Backward (criterion: Probability of F-to-remove >= ,100).

a  All requested variables entered.

b  Dependent Variable: Qualprod

        Model Summary(c)

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

,976(a)

,952

,945

2,5823

2

,976(b)

,952

,947

2,5326

a  Predictors: (Constant), Qualraw, Temp2, Recycle, Temp1

b  Predictors: (Constant), Qualraw, Recycle, Temp1

c  Dependent Variable: Qualprod

        ANOVA(c)

Model

Sum of Squares

Df

Mean Square

F

Sig.

1

Regression

3322,691

4

830,673

124,570

,000(a)

Residual

166,708

25

6,668

Total

3489,399

29

2

Regression

3322,639

3

1107,546

172,681

,000(b)

Residual

166,760

26

6,414

Total

3489,399

29

a  Predictors: (Constant), Qualraw, Temp2, Recycle, Temp1

b  Predictors: (Constant), Qualraw, Recycle, Temp1

c  Dependent Variable: Qualprod

        Coefficients(a)

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-10,354

7,686

-1,347

,190

Temp1

,041

,014

,277

3,007

,006

Temp2

,002

,025

,008

,088

,931

Recycle

,671

,390

,152

1,720

,098

Qualraw

,620

,090

,666

6,911

,000

2

(Constant)

-9,726

2,796

-3,478

,002

Temp1

,041

,013

,278

3,100

,005

Recycle

,642

,210

,145

3,056

,005

Qualraw

,620

,088

,665

7,053

,000

a  Dependent Variable: Qualprod

        Variables Entered/Removed(a)

Model

Variables Entered

Variables Removed

Method

1

Qualraw

.

Forward (Criterion: Probability-of-F-to-enter <= ,050)

2

Temp1

.

Forward (Criterion: Probability-of-F-to-enter <= ,050)

3

Recycle

.

Forward (Criterion: Probability-of-F-to-enter <= ,050)

a  Dependent Variable: Qualprod

        Model Summary(d)

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

,961(a)

,924

,921

3,0767

2

,967(b)

,935

,930

2,8974

3

,976(c)

,952

,947

2,5326

a  Predictors: (Constant), Qualraw

b  Predictors: (Constant), Qualraw, Temp1

c  Predictors: (Constant), Qualraw, Temp1, Recycle

d  Dependent Variable: Qualprod

        ANOVA(d)

Model

Sum of Squares

Df

Mean Square

F

Sig.

1

...read more.

Conclusion

class="c1">-3,478

,002

Qualraw

,620

,088

,665

7,053

,000

Temp1

,041

,013

,278

3,100

,005

Recycle

,642

,210

,145

3,056

,005

a  Dependent Variable: Qualprod

APPENDIX Q1b        

        Coefficients(a)

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

-10,354

7,686

-1,347

,190

Temp1

,041

,014

,277

3,007

,006

,225

4,442

Temp2

,002

,025

,008

,088

,931

,260

3,839

Recycle

,671

,390

,152

1,720

,098

,246

4,067

Qualraw

,620

,090

,666

6,911

,000

,206

4,858

2

(Constant)

-9,726

2,796

-3,478

,002

Temp1

,041

,013

,278

3,100

,005

,228

4,378

Recycle

,642

,210

,145

3,056

,005

,814

1,228

Qualraw

,620

,088

,665

7,053

,000

,207

4,841

a  Dependent Variable: Qualprod


APPENDIX Q2a

Means

Case Processing Summary

Cases

Included

Excluded

Total

N

Percent

N

Percent

N

Percent

Qualprod  * Shift

30

100,0%

0

,0%

30

100,0%

        Report

Qualprod

Shift

N

Mean

Median

Std. Deviation

Minimum

Maximum

Range

Dayshift

16

11,206

11,550

4,8480

2,6

18,3

15,7

Nightshift

14

30,036

29,000

6,1366

22,4

45,8

23,4

Total

30

19,993

18,200

10,9692

2,6

45,8

43,2

T-Test

        Group Statistics

Shift

N

Mean

Std. Deviation

Std. Error Mean

Qualprod

Dayshift

16

11,206

4,8480

1,2120

Nightshift

14

30,036

6,1366

1,6401

                      Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig.

(2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Qual

prod

Equal variances assumed

,141

,711

-9,382

28

,000

-18,8295

2,0070

-22,9405

-14,7184

Equal variances not assumed

-9,233

24,693

,000

-18,8295

2,0393

-23,0322

-14,6268


APPENDIX Q2b

        Variables Entered/Removed(b)

Model

Variables Entered

Variables Removed

Method

1

Shift, Temp2, Qualraw, Recycle, Temp1(a)

.

Enter

a  All requested variables entered.

b  Dependent Variable: Qualprod

        Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

,976(a)

,953

,944

2,6033

a  Predictors: (Constant), Shift, Temp2, Qualraw, Recycle, Temp1

        ANOVA(b)

Model

Sum of Squares

Df

Mean Square

F

Sig.

1

Regression

3326,751

5

665,350

98,178

,000(a)

Residual

162,648

24

6,777

Total

3489,399

29

a  Predictors: (Constant), Shift, Temp2, Qualraw, Recycle, Temp1

b  Dependent Variable: Qualprod

        Coefficients(a)

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-9,677

7,798

-1,241

,227

Temp1

,035

,015

,241

2,318

,029

Temp2

,006

,026

,019

,220

,827

Recycle

,666

,393

,151

1,695

,103

Qualraw

,594

,096

,638

6,163

,000

Shift

1,596

2,062

,074

,774

,446

a  Dependent Variable: Qualprod

...read more.

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