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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.

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

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 Qualprod 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

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