Defects After Delivery

Defects After Delivery

Datasheet: Defects After Delivery
Defects per million items received from suppliers
Month 2010 2011
January 812 828
February 810 832
March 813 847
April 823 839
May 832 832
June 848 840
July 837 849
August 831 857
September 827
October 838
November 826
December 819
Assigning numbers 1 through 20 for each month from January 2010 through August 2011.
SIMPLE LINEAR REGRESSION:
Month Defects
1 812
2 810
3 813
4 823
5 832
6 848
7 837
8 831
9 827
10 838
11 826
12 819
13 828
14 832
15 847
16 839
17 832
18 840
19 849
20 857 The scatterplot shows that a linear model can fit the data.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.6994187048
R Square 0.4891865246
Adjusted R Square 0.4608079981
Standard Error 9.4427395385
Observations 20
ANOVA
df SS MS F Significance F
Regression 1 1537.0240601504 1537.0240601504 17.2379114202 0.0005989968
Residual 18 1604.9759398496 89.1653299916
Total 19 3142
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 816.0368421053 4.3864495472 186.0358436435 5.14111788361825E-31 806.8212535732 825.2524306373
Month 1.5203007519 0.3661737333 4.1518563824 0.0005989968 0.7509982849 2.2896032188
RESIDUAL OUTPUT
Observation Predicted Defects Residuals Standard Residuals
1 817.5571428571 -5.5571428571 -0.6046361353
2 819.077443609 -9.077443609 -0.9876568882
3 820.5977443609 -7.5977443609 -0.8266605529
4 822.1180451128 0.8819548872 0.0959597059
5 823.6383458647 8.3616541353 0.9097765472 The residual plot shows an apparent pattern indicating that there is good evidence that
6 825.1586466165 22.8413533835 2.485217312 some other functional form might better fit the data than the linear form.
7 826.6789473684 10.3210526316 1.1229658001
8 828.1992481203 2.8007518797 0.3047313765
9 829.7195488722 -2.7195488722 -0.2958962118
10 831.2398496241 6.7601503759 0.7355274648
11 832.7601503759 -6.7601503759 -0.7355274648
12 834.2804511278 -15.2804511278 -1.662565306 Bin Frequency
13 835.8007518797 -7.8007518797 -0.8487484648 -1.662565306 1
14 837.3210526316 -5.3210526316 -0.5789487118 -0.6256196515 5
15 838.8413533835 8.1586466165 0.8876886353 0.411326003 7
16 840.3616541353 -1.3616541353 -0.1481526236 1.4482716575 6
17 841.8819548872 -9.8819548872 -1.0751904649 More 1
18 843.4022556391 -3.4022556391 -0.3701770413
19 844.922556391 4.077443609 0.4436398
20 846.4428571429 10.5571428571 1.1486532235
POLYNOMIAL REGRESSION OF ORDER 3:
Defects Month Month^2 Month^3
812 1 1 1
810 2 4 8
813 3 9 27
823 4 16 64
832 5 25 125
848 6 36 216
837 7 49 343
831 8 64 512
827 9 81 729
838 10 100 1000
826 11 121 1331
819 12 144 1728
828 13 169 2197
832 14 196 2744
847 15 225 3375
839 16 256 4096
832 17 289 4913
840 18 324 5832 Curvilinear regression model of order 3 fits the data better than that of order 2 as suggested by the scatterplot.
849 19 361 6859
857 20 400 8000
Correlation Matrix:
Defects Month Month^2 Month^3
Defects 1 The correlations between the independent variables exceed 0.7, the recommended value suggesting that the problem of multicollinearity exists for obvious reason
Month 0.6994187048 1 that the independent variables in the regression model contain high levels of the same information as two of them are derived from the first independent variable.
Month^2 0.67681915 0.9713482022 1
Month^3 0.6683502353 0.9220503041 0.9864798137 1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8334429634
R Square 0.6946271733
Adjusted R Square 0.6373697683
Standard Error 7.7438742788
Observations 20
ANOVA
df SS MS F Significance F 69.46% of the variation in Defects is explained by the model.
Regression 3 2182.5185784736 727.5061928245 12.1316565637 0.0002154423 The p-value for overall significance of the model is 0.0002 which is less than 0.05, the level
Residual 16 959.4814215264 59.9675888454 of significance. Therefore, we reject the null hypothesis at the 5% level of significance and conclude that at least one slope coefficient in the
Total 19 3142 model is different from zero. And we observe that, at the 5% level of significance, all the independent variables are
statistically significant in explaining the variation in Defects using the p-values.
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 795.3715170279 8.4588804603 94.0279887823 2.22849284162433E-23 777.4394915147 813.303542541
Month 11.9816011974 3.4035402616 3.5203347916 0.0028389555 4.7664181608 19.1967842341
Month^2 -1.2089707529 0.3718285299 -3.251420092 0.0050060303 -1.9972120238 -0.4207294819
Month^3 0.0382353621 0.0116573515 3.2799355915 0.0047143776 0.0135228809 0.0629478433
RESIDUAL OUTPUT
Observation Predicted Defects Residuals Standard Residuals (ei – ei-1)^2
1 806.1823828346 5.8176171654 0.8186601565
2 814.8047193082 -4.8047193082 -0.6761242875 112.8340321583
3 821.4679386213 -8.4679386213 -1.1916157011 13.4191757359
4 826.4014529465 -3.4014529465 -0.4786554224 25.6692770927
5 829.8346744564 2.1653255436 0.3047064972 30.9890227573
6 831.9970153237 16.0029846763 2.2519539473 191.4808102733
7 833.1178877209 3.8821122791 0.5462942225 146.9155476697
8 833.4267038207 -2.4267038207 -0.3414878761 39.8011605807
9 833.1528757956 -6.1528757956 -0.8658380431 13.8843575867
10 832.5258158183 5.4741841817 0.7703319678 135.1885237159
11 831.7749360614 -5.7749360614 -0.8126540344 126.5427062429 Bin Frequency
12 831.1296486974 -12.1296486974 -1.7068947335 40.3823726867 -1.7068947335 1
13 830.8193658991 -2.8193658991 -0.3967436259 86.6813657856 -0.7171825633 4
14 831.0734998389 0.9265001611 0.1303779099 14.0315125408 0.2725296069 8
15 832.1214626895 14.8785373105 2.0937207343 194.6593406175 1.2622417771 5
16 834.1926666235 4.8073333765 0.6764921415 101.429148681 More 2
17 837.5165238136 -5.5165238136 -0.7762900377 106.5820272807
18 842.3224464323 -2.3224464323 -0.3268166855 10.2021303178
19 848.8398466522 0.1601533478 0.0225369186 6.1633016681
20 857.298136646 -0.298136646 -0.0419540486 0.2100297184
959.4814215264 1397.0658431101
Durbin-Watson statistic D 1.456 indicating that the test is inconclusive and hence cannot be concluded that errors are independent.
The number of defects in the materials received from the suppliers might have increased each month had the supplier initiative by the company not been implemented in August 2009
because the predictions for the number of defects using the above model are increasing each month.

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

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Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Month Residual Plot

Residuals -5.5571428571429351 -9.0774436090225663 -7.5977443609023112 0.88195488721805759 8.3616541353383127 22.841353383458568 10.321052631578937 2.8007518796991917 -2.7195488721804395 6.7601503759398156 -6.7601503759399293 -15.28045112781956 -7.8007518796993054 -5.3210526315789366 8.1586466165413185 -1.3616541353383127 -9.8819548872180576 -3.4022556390978025 4.0774436090225663 10.557142857142821Month

Residuals

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^2

Residuals

Month^3 Residual Plot

1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 5.8176171654432665 -4.8047193081516752 -8.4679386212566214 -3.4014529464791394 2.1653255435730898 16.002984676292044 3.8821122790701565 -2.4267038207002543 -6.1528757956272102 5.4741841816818351 -5.7749360613810268 -12.12964869742359 -2.8193658990536505 0.92650016112122557 14.87853731049313 4.8073333764544941 -5.5165238136028165 -2.3224464322862559 0.16015334779638124 -0.29813664596269973Month^3

Residuals

Standard residuals

Frequency -1.662565306 -0.625619652 0.411326003 1.448271658 More 1 5 7 6 1Bin

Frequency

Standard residuals

Frequency -1.706894733 -0.717182563 0.272529607 1.262241777 More 1 4 8 5 2Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857Month

Defects

Defects After Delivery_2

Datasheet: 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
Assigning numbers 1 through 60 for each month from January 2008 through December 2012.
Month Defects
1 812
2 810
3 813
4 823
5 832
6 848
7 837
8 831
9 827
10 838
11 826
12 819
13 828
14 832
15 847
16 839
17 832
18 840
19 849
20 857
21 839
22 842
23 828
24 816
25 824
26 836
27 818
28 825
29 804
30 812 The scatterplot suggests that a curvilinear regression model fits the data better than a linear model.
31 806
32 798
33 804
34 713
35 705
36 686
37 682
38 695
39 692
40 686
41 673
42 681
43 696
44 688
45 671
46 645
47 617
48 603
49 571
50 575
51 547
52 542
53 532
54 496
55 472
56 460
57 441
58 445
59 438
60 436
Polynomial Regression of Order 2:
Defects Month Month^2 SUMMARY OUTPUT
812 1 1
810 2 4 Regression Statistics The estimated regression model is:
813 3 9 Multiple R 0.9884246381 Defects^ = 803.736 + 5.634Month – 0.205Month^2
823 4 16 R Square 0.9769832652
832 5 25 Adjusted R Square 0.9761756605 The coefficient for Month represents the linear effect of Month on Defects and
848 6 36 Standard Error 20.6944209481 the coefficient for Month^2 represents the curvilinear effect of Month on Defects.
837 7 49 Observations 60
831 8 64
827 9 81 ANOVA The residuals exhibit no apparent patterns in the residual plots and the distribution for the standard residuals
838 10 100 df SS MS F Significance F appears to be normal (eliminating the outliers on the left).
826 11 121 Regression 2 1036155.23367256 518077.61683628 1209.7295006455 2.08087420337233E-47
819 12 144 Residual 57 24410.7663274405 428.2590583761 97.7% of the variation in the dependent variable Defects is explained by the model.
828 13 169 Total 59 1060566
832 14 196 The variation around the regression line given by the standard error of the estimate (20.7) is very much less than
847 15 225 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% the variation around the sample mean or the standard deviation of Defects.
839 16 256 Intercept 803.7361776739 8.2897035159 96.9559618304 5.70463277795146E-65 787.1363327155 820.3360226323 This indicates that the independent variable in the regression model explains much of the variation.
832 17 289 Month 5.6338085817 0.6270482254 8.9846495911 0 4.3781661691 6.8894509944
840 18 324 Month^2 -0.2053114804 0.0099635279 -20.6063035457 4.30356630249347E-28 -0.2252631008 -0.1853598599 The p-value for overall significance of the model is zero which is less than any level
849 19 361 of significance. Therefore, we reject the null hypothesis and conclude that at least one slope coefficient in the
857 20 400 model is different from zero. And we observe that, at any level of significance, both the independent variables are
839 21 441 statistically significant in explaining the variation in Defects with a p-value of zero.
842 22 484 RESIDUAL OUTPUT The number of defects can further be reduced in the near future by continuing with the supplier initiative that has
828 23 529 been implemented in August 2009 because the predicted number of defects using this model
816 24 576 Observation Predicted Defects Residuals Standard Residuals (ei – ei-1)^2 are declining each month.
824 25 625 1 809.1646747753 2.8353252247 0.1393921063
836 26 676 2 814.1825489159 -4.1825489159 -0.2056251954 49.2505574542
818 27 729 3 818.7898000959 -5.7898000959 -0.2846419253 2.5832563555
825 28 784 4 822.9864283151 0.0135716849 0.00066722 33.6791240256
804 29 841 5 826.7724335737 5.2275664263 0.2570010272 27.185741164
812 30 900 6 830.1478158715 17.8521841285 0.8776607096 159.380972126
806 31 961 7 833.1125752086 3.8874247914 0.1911161108 195.0145033436
798 32 1024 8 835.666711585 -4.666711585 -0.229427916 73.1732491462
804 33 1089 9 837.8102250007 -10.8102250007 -0.531459326 37.7427570888
713 34 1156 10 839.5431154557 -1.5431154557 -0.0758636476 85.8793193193
705 35 1225 11 840.86538295 -14.86538295 -0.7308216437 177.4828111891
686 36 1296 12 841.7770274835 -22.7770274835 -1.1197790679 62.5941192255
682 37 1369 13 842.2780490564 -14.2780490564 -0.701946752 72.232634305
695 38 1444 14 842.3684476685 -10.3684476685 -0.5097403809 15.2849830119
692 39 1521 15 842.04822332 4.95177668 0.243442472 234.7092740903
686 40 1600 16 841.3173760107 -2.3173760107 -0.1139283496 52.8405808411
673 41 1681 17 840.1759057407 -8.1759057407 -0.4019492059 34.3223705975 Bin Frequency
681 42 1764 18 838.62381251 1.37618749 0.0676570262 91.2424850878 -2.6778703675 1
696 43 1849 19 836.6610963186 12.3389036814 0.6066132235 120.1811462932 -2.0289096752 3
688 44 1936 20 834.2877571665 22.7122428335 1.1165940827 107.6061651648 -1.3799489829 0
671 45 2025 21 831.5037950537 7.4962049463 0.3685333125 231.527808984 -0.7309882906 8
645 46 2116 22 828.3092099802 13.6907900198 0.6730755406 38.3728842332 -0.0820275983 13
617 47 2209 23 824.7040019459 3.2959980541 0.1620400042 108.0517000114 0.566933094 18
603 48 2304 24 820.688170951 -4.688170951 -0.2304829154 63.7469547012 1.2158937863 11
571 49 2401 25 816.2617169953 7.7382830047 0.3804345118 154.4167579122 More 6
575 50 2500 26 811.4246400789 24.5753599211 1.2081898591 283.4871590878
547 51 2601 27 806.1769402018 11.8230597982 0.5812529703 162.621158425
542 52 2704 28 800.518617364 24.481382636 1.2035696865 160.2331370658 Durbin-Watson statistic D:
532 53 2809 29 794.4496715655 9.5503284345 0.46951947 222.9363795681 0.6103996299 suggests that autocorrelation exists.
496 54 2916 30 787.9701028063 24.0298971937 1.181373465 209.6579114528
472 55 3025 31 781.0799110864 24.9200889136 1.2251376504 0.7924412982
460 56 3136 32 773.7790964058 24.2209035942 1.1907638461 0.4888601108
441 57 3249 33 766.0676587644 37.9323412356 1.8648544786 188.0035221924
445 58 3364 34 757.9455981624 -44.9455981624 -2.2096447858 6868.7528388499
438 59 3481 35 749.4129145996 -44.4129145996 -2.1834566494 0.283751778
436 60 3600 36 740.4696080762 -54.4696080762 -2.6778703675 101.1370836808
37 731.115678592 -49.115678592 -2.4146569973 28.6645609216
38 721.3511261471 -26.3511261471 -1.2954912354 518.2248480162
39 711.1759507415 -19.1759507415 -0.9427405864 51.4831421012
40 700.5901523752 -14.5901523752 -0.7172905788 21.0295466565
41 689.5937310481 -16.5937310481 -0.8157918191 4.0143274988
42 678.1866867604 2.8133132396 0.1383099388 376.633367986
43 666.369019512 29.630980488 1.4567375719 719.1872766481
44 654.1407293028 33.8592706972 1.6646115305 17.8784380928
45 641.501816133 29.498183867 1.4502089379 19.01907834
46 628.4522800024 16.5477199976 0.8135297939 167.7145144334
47 614.9921209111 2.0078790889 0.0987126602 211.4069736509
48 601.1213388591 1.8786611409 0.0923599632 0.0166972781
49 586.8399338464 -15.8399338464 -0.7787331499 313.9486083239
50 572.147905873 2.852094127 0.14021651 349.3919097588
51 557.0452549389 -10.0452549389 -0.4938513693 166.3416129271
52 541.531981044 0.468018956 0.0230090529 110.5289279877
53 525.6080841885 6.3919158115 0.3142435304 35.0925539551
54 509.2735643723 -13.2735643723 -0.6525636214 386.7311108574
55 492.5284215953 -20.5284215953 -1.0092316399 52.6329533267
56 475.3726558576 -15.3726558576 -0.7557605249 26.5819203417
57 457.8062671592 -16.8062671592 -0.8262406579 2.0552413641
58 439.8292555002 5.1707444998 0.2542075106 482.9890414638
59 421.4416208804 16.5583791196 0.8140538246 129.6782222341
60 402.6433632998 33.3566367002 1.6399007104 282.1814577412
24410.7663274405 14900.3227310864

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857 839 842 828 816 824 836 818 825 804 812 806 798 804 713 705 686 682 695 692 686 673 681 696 688 671 645 617 603 571 575 547 542 532 496 472 460 441 445 438 436Month

Defects

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2.8353252247488854 -4.1825489159174367 -5.7898000958738294 1.3571684879707391E-2 5.227566426343401 17.852184128516797 3.8874247914002353 -4.6667115850063965 -10.810225000703099 -1.5431154556898719 -14.865382949966488 -22.777027483533402 -14.278049056390273 -10.368447668537101 4.9517766800258869 -2.3173760107011958 -8.1759057407182354 1.3761874899746545 12.33890368137736 22.712242833490109 7.4962049463129006 13.690790019845508 3.2959980540881588 -4.6881709509592611 7.7382830047031348 24.575359921075574 11.823059798158056 24.481382635950467 9.5503284344528083 24.029897193664965 24.920088913587165 24.220903594219294 37.932341235561466 -44.945598162386545 -44.412914599624514 -54.469608076152554 -49.115678591970664 -26.351126147078958 -19.175950741476981 -14.590152375165417 -16.593731048143582 2.8133132395880693 29.630980488029536 33.859270697181046 29.498183867042485 16.547719997614195 2.007879088895379 1.8786611408867202 -15.839933846412009 2.8520941269991908 -10.04525493887968 0.46801895595137921 6.3919158114925949 -13.273564372256374 -20.528421595295413 -15.372655857624522 -16.806267159243703 5.1707444998472738 16.558379119647952 33.356636700158674Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 841 900 961 1024 1089 1156 1225 1296 1369 1444 1521 1600 1681 1764 1849 1936 2025 2116 2209 2304 2401 2500 2601 2704 2809 2916 3025 3136 3249 3364 3481 3600 2.8353252247488854 -4.1825489159174367 -5.7898000958738294 1.3571684879707391E-2 5.227566426343401 17.852184128516797 3.8874247914002353 -4.6667115850063965 -10.810225000703099 -1.5431154556898719 -14.865382949966488 -22.777027483533402 -14.278049056390273 -10.368447668537101 4.9517766800258869 -2.3173760107011958 -8.1759057407182354 1.3761874899746545 12.33890368137736 22.712242833490109 7.4962049463129006 13.690790019845508 3.2959980540881588 -4.6881709509592611 7.7382830047031348 24.575359921075574 11.823059798158056 24.481382635950467 9.5503284344528083 24.029897193664965 24.920088913587165 24.220903594219294 37.932341235561466 -44.945598162386545 -44.412914599624514 -54.469608076152554 -49.115678591970664 -26.351126147078958 -19.175950741476981 -14.590152375165417 -16.593731048143582 2.8133132395880693 29.630980488029536 33.859270697181046 29.498183867042485 16.547719997614195 2.007879088895379 1.8786611408867202 -15.839933846412009 2.8520941269991908 -10.04525493887968 0.46801895595137921 6.3919158114925949 -13.273564372256374 -20.528421595295413 -15.372655857624522 -16.806267159243703 5.1707444998472738 16.558379119647952 33.356636700158674Month^2

Residuals

Standard residual

Frequency -2.677870368 -2.028909675 -1.379948983 -0.730988291 -0.082027598 0.566933094 1.215893786 More 1 3 0 8 13 18 11 6Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857 839 842 828 816 824 836 818 825 804 812 806 798 804 713 705 686 682 695 692 686 673 681 696 688 671 645 617 603 571 575 547 542 532 496 472 460 441 445 438 436Month

Defects

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2.8353252247488854 -4.1825489159174367 -5.7898000958738294 1.3571684879707391E-2 5.227566426343401 17.852184128516797 3.8874247914002353 -4.6667115850063965 -10.810225000703099 -1.5431154556898719 -14.865382949966488 -22.777027483533402 -14.278049056390273 -10.368447668537101 4.9517766800258869 -2.3173760107011958 -8.1759057407182354 1.3761874899746545 12.33890368137736 22.712242833490109 7.4962049463129006 13.690790019845508 3.2959980540881588 -4.6881709509592611 7.7382830047031348 24.575359921075574 11.823059798158056 24.481382635950467 9.5503284344528083 24.029897193664965 24.920088913587165 24.220903594219294 37.932341235561466 -44.945598162386545 -44.412914599624514 -54.469608076152554 -49.115678591970664 -26.351126147078958 -19.175950741476981 -14.590152375165417 -16.593731048143582 2.8133132395880693 29.630980488029536 33.859270697181046 29.498183867042485 16.547719997614195 2.007879088895379 1.8786611408867202 -15.839933846412009 2.8520941269991908 -10.04525493887968 0.46801895595137921 6.3919158114925949 -13.273564372256374 -20.528421595295413 -15.372655857624522 -16.806267159243703 5.1707444998472738 16.558379119647952 33.356636700158674Month

Residuals

Month^2 Residual Plot

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 841 900 961 1024 1089 1156 1225 1296 1369 1444 1521 1600 1681 1764 1849 1936 2025 2116 2209 2304 2401 2500 2601 2704 2809 2916 3025 3136 3249 3364 3481 3600 2.8353252247488854 -4.1825489159174367 -5.7898000958738294 1.3571684879707391E-2 5.227566426343401 17.852184128516797 3.8874247914002353 -4.6667115850063965 -10.810225000703099 -1.5431154556898719 -14.865382949966488 -22.777027483533402 -14.278049056390273 -10.368447668537101 4.9517766800258869 -2.3173760107011958 -8.1759057407182354 1.3761874899746545 12.33890368137736 22.712242833490109 7.4962049463129006 13.690790019845508 3.2959980540881588 -4.6881709509592611 7.7382830047031348 24.575359921075574 11.823059798158056 24.481382635950467 9.5503284344528083 24.029897193664965 24.920088913587165 24.220903594219294 37.932341235561466 -44.945598162386545 -44.412914599624514 -54.469608076152554 -49.115678591970664 -26.351126147078958 -19.175950741476981 -14.590152375165417 -16.593731048143582 2.8133132395880693 29.630980488029536 33.859270697181046 29.498183867042485 16.547719997614195 2.007879088895379 1.8786611408867202 -15.839933846412009 2.8520941269991908 -10.04525493887968 0.46801895595137921 6.3919158114925949 -13.273564372256374 -20.528421595295413 -15.372655857624522 -16.806267159243703 5.1707444998472738 16.558379119647952 33.356636700158674Month^2

Residuals

Standard residual

Frequency -2.677870368 -2.028909675 -1.379948983 -0.730988291 -0.082027598 0.566933094 1.215893786 More 1 3 0 8 13 18 11 6Bin

Frequency

Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857 839 842 828 816 824 836 818 825 804 812 806 798 804 713 705 686 682 695 692 686 673 681 696 688 671 645 617 603 571 575 547 542 532 496 472 460 441 445 438 436Month

Defects

Month Residual Plot

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2.8353252247488854 -4.1825489159174367 -5.7898000958738294 1.3571684879707391E-2 5.227566426343401 17.852184128516797 3.8874247914002353 -4.6667115850063965 -10.810225000703099 -1.5431154556898719 -14.865382949966488 -22.777027483533402 -14.278049056390273 -10.368447668537101 4.9517766800258869 -2.3173760107011958 -8.1759057407182354 1.3761874899746545 12.33890368137736 22.712242833490109 7.4962049463129006 13.690790019845508 3.2959980540881588 -4.6881709509592611 7.7382830047031348 24.575359921075574 11.823059798158056 24.481382635950467 9.5503284344528083 24.029897193664965 24.92008891358