In reviewing the PLE data, Elizabeth Burke noticed that defects received from su

Question

In reviewing the PLE data, Elizabeth Burke noticed that defects received from suppliers have decreased (worksheet Defects After Delivery). Upon investigation, she learned that in 2010, PLE experienced some quality problems due to an increasing number of defects in materials received from suppliers. The company instituted an initiative in August 2011 to work with suppliers to reduce these defects, to more closely coordinate deliveries, and to improve materials quality through reengineering supplier production policies. Elizabeth noted that the program appeared to reverse an increasing trend in defects; she would like to predict what might have happened had the supplier initiative not been implemented and how the number of defects might further be reduced in the near future.

Use techniques of regression analysis to assist her in evaluating the data in the worksheet Defects After Delivery. Summarize your work in a formal report with all appropriate results and analyses.

Defects After Delivery Defects per million items received from suppliers Month 2010 2011 2012 2013 2014 January 812 828 824 682 571 February 810 832 836 695 575 March 813 847 818 692 547 April 823 839 825 686 542 May 832 832 804 673 532 June 848 840 812 681 496 July 837 849 806 696 472 August 831 857 798 688 460 September 827 839 804 671 441 October 838 842 713 645 445 November 826 828 705 617 438 December 819 816 686 603 436

Explanation / Answer

We created 11 dummy variables for the month with January as the reference month and ran the regression of defect on Year and 11 dummy variables and the resutls gave the estimated regression model as

Defect= 167437.6-82.85 Year +6.2 February +0.00*March-0.4 April -8.8 May – 8 June -11.4 July

-16.6 August -27 September -46.8 October -60.6 November -71.4 December

The regression model explained 81% of the variability in number of defect. Years of manufacturing has significant effect on defects as p-value of test of coefficient is less than 0.05. However, all months coefficients are insignificant with p<0.05. So months do not help predicting the defect. Corresponding to one year increase in years, the number of defects decrease by 82.85 Defects per million items received from suppliers, holding other predictors fixed.

SUMMARY OUTPUT Regression Statistics Multiple R 0.90054579 R Square 0.810982721 Adjusted R Square 0.76272299 Standard Error 65.30864528 Observations 60 ANOVA df SS MS F Significance F Regression 12 860100.7 71675.05833 16.80454294 3.96016E-13 Residual 47 200465.3 4265.219149 Total 59 1060566 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 167437.6 11995.25033 13.95865825 2.45248E-18 143306.2689 191568.9311 Year -82.85 5.96183637 -13.89672491 2.90421E-18 -94.84366776 -70.85633224 February 6.2 41.304814 0.150103569 0.881325225 -76.89456774 89.29456774 March 9.95682E-15 41.304814 2.41057E-16 1 -83.09456774 83.09456774 April -0.4 41.304814 -0.009684101 0.992314316 -83.49456774 82.69456774 May -8.8 41.304814 -0.213050227 0.832209215 -91.89456774 74.29456774 June -8 41.304814 -0.193682025 0.847259512 -91.09456774 75.09456774 July -11.4 41.304814 -0.275996885 0.783760427 -94.49456774 71.69456774 August -16.6 41.304814 -0.401890201 0.68958661 -99.69456774 66.49456774 September -27 41.304814 -0.653676833 0.516505564 -110.0945677 56.09456774 October -46.8 41.304814 -1.133039844 0.262944473 -129.8945677 36.29456774 November -60.6 41.304814 -1.467141336 0.14899769 -143.6945677 22.49456774 December -71.4 41.304814 -1.728612069 0.090443519 -154.4945677 11.69456774

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