business statistics 7:2

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Regression old and new process

Old Process New Process
SUMMARY OUTPUT (Old Process)
Week Elapsed Time Week Test Week Elapsed Time
1 31.7 13 1 24 Regression Statistics
2 27 14 2 25.8 Multiple R 0.5745518821
3 33.8 15 3 31 R Square 0.3301098652
4 30 16 4 23.5 Adjusted R Square 0.2631208517
5 32.5 17 5 28.5 Standard Error 3.4883134897
6 33.5 18 6 25.6 Observations 12
7 38.2 19 7 28.7
8 37.5 20 8 27.4 ANOVA
9 29 21 9 28.5 df SS MS F Significance F
10 31.3 22 10 25.2 Regression 1 59.9633566434 59.9633566434 4.9278209667 0.0507057521
11 38.6 23 11 24.5 Residual 10 121.6833100233 12.1683310023
12 39.3 24 12 23.5 Total 11 181.6466666667
Average 33.53 26.35 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
standard Deviation 4.06 2.43 b0 29.3242424242 2.1469085422 13.6588223705 0.0000000857 24.5406320896 34.1078527589 24.5406320896 34.1078527589
b1 0.6475524476 0.2917074284 2.2198695833 0.0507057521 -0.0024122071 1.2975171022 -0.0024122071 1.2975171022
RESIDUAL OUTPUT
Observation Actual Y Predicted Y Residuals
1 31.7 29.9717948718 1.7282051282
2 27 30.6193473193 -3.6193473193
3 33.8 31.2668997669 2.5331002331
4 30 31.9144522145 -1.9144522145
5 32.5 32.562004662 -0.062004662
6 33.5 33.2095571096 0.2904428904
7 38.2 33.8571095571 4.3428904429
8 37.5 34.5046620047 2.9953379953
9 29 35.1522144522 -6.1522144522
10 31.3 35.7997668998 -4.4997668998
Process Improvement 11 38.6 36.4473193473 2.1526806527
-2.22 12 39.3 37.0948717949 2.2051282051
-0 Total residue error
SUMMARY OUTPUT (New Process)
Regression Statistics
Multiple R 0.1713144422
R Square 0.0293486381
Adjusted R Square -0.0677164981
Standard Error 2.5093057575
Observations 12
ANOVA
df SS MS F Significance F
Regression 1 1.9038461538 1.9038461538 0.3023602424 0.5944737741
Residual 10 62.9661538462 6.2966153846
Total 11 64.87
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
b0 27.1 1.5443709351 17.5475977854 0.0000000077 23.6589271177 30.5410728823 23.6589271177 30.5410728823
b1 -0.1153846154 0.209838689 -0.5498729329 0.5944737741 -0.5829343511 0.3521651203 -0.5829343511 0.3521651203
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 26.9846153846 -2.9846153846
2 26.8692307692 -1.0692307692
3 26.7538461538 4.2461538462
4 26.6384615385 -3.1384615385
5 26.5230769231 1.9769230769
6 26.4076923077 -0.8076923077
7 26.2923076923 2.4076923077
8 26.1769230769 1.2230769231
9 26.0615384615 2.4384615385
10 25.9461538462 -0.7461538462
11 25.8307692308 -1.3307692308
12 25.7153846154 -2.2153846154
Old Process New Process
Elapsed Time Elapsed Time
Week Test Week
1 31.7 0.6475524476 31.0524475524 1 24 -0.1153846154 24.1153846154
2 27 1.2951048951 25.7048951049 2 25.8 -0.2307692308 26.0307692308
3 33.8 1.9426573427 31.8573426573 3 31 -0.3461538462 31.3461538462
4 30 2.5902097902 27.4097902098 4 23.5 -0.4615384615 23.9615384615
5 32.5 3.2377622378 29.2622377622 5 28.5 -0.5769230769 29.0769230769
6 33.5 3.8853146853 29.6146853147 6 25.6 -0.6923076923 26.2923076923
7 38.2 4.5328671329 33.6671328671 7 28.7 -0.8076923077 29.5076923077
8 37.5 5.1804195804 32.3195804196 8 27.4 -0.9230769231 28.3230769231
9 29 5.827972028 23.172027972 9 28.5 -1.0384615385 29.5384615385
10 31.3 6.4755244755 24.8244755245 10 25.2 -1.1538461538 26.3538461538
11 38.6 7.1230769231 31.4769230769 11 24.5 -1.2692307692 25.7692307692
12 39.3 7.7706293706 31.5293706294 12 23.5 -1.3846153846 24.8846153846
29.3242424242 27.1
Process differences during test period 0.76 2.22

Old Process

Y 1 2 3 4 5 6 7 8 9 10 11 12 31.7 27 33.799999999999997 30 32.5 33.5 38.200000000000003 37.5 29 31.3 38.6 39.299999999999997 Predicted Y

y = 0.6476x + 29.324

1 2 3 4 5 6 7 8 9 10 11 12 29.971794871794874 30.619347319347323 31.266899766899769 31.914452214452218 32.562004662004668 33.20955710955711 33.85710955710956 34.504662004662009 35.152214452214459 35.799766899766901 36.44731934731935 37.0948717948718

Test week number

elapsed time (day)

X Variable 1 Line Fit Plot

Y 1 2 3 4 5 6 7 8 9 10 11 12 24 25.8 31 23.5 28.5 25.6 28.7 27.4 28.5 25.2 24.5 23.5 Predicted Y 1 2 3 4 5 6 7 8 9 10 11 12 26.984615384615381 26.869230769230768 26.753846153846151 26.638461538461534 26.523076923076921 26.407692307692304 26.292307692307688 26.176923076923075 26.061538461538458 25.946153846153845 25.830769230769228 25.715384615384611

X Variable 1

Y

New Process

Y 1 2 3 4 5 6 7 8 9 10 11 12 24 25.8 31 23.5 28.5 25.6 28.7 27.4 28.5 25.2 24.5 23.5 Predicted Y

y = -0.1154x + 27.1

1 2 3 4 5 6 7 8 9 10 11 12 26.984615384615381 26.869230769230768 26.753846153846151 26.638461538461534 26.523076923076921 26.407692307692304 26.292307692307688 26.176923076923075 26.061538461538458 25.946153846153845 25.830769230769228 25.715384615384611

Test week number

elapsed time (day)

Old vs. new process

Old Process New Process
Elapsed Time Elapsed Time SUMMARY OUTPUT
Week Week Test Week
1 31.7 13 1 24 Regression Statistics
2 27 14 2 25.8 Multiple R 0.0077382654
3 33.8 15 3 31 R Square 0.0000598808
4 30 16 4 23.5 Adjusted R Square -0.0999341312
5 32.5 17 5 28.5 Standard Error 2.546882713
6 33.5 18 6 25.6 Observations 12
7 38.2 19 7 28.7
8 37.5 20 8 27.4 ANOVA
9 29 21 9 28.5 df SS MS F Significance F
10 31.3 22 10 25.2 Regression 1 0.0038844643 0.0038844643 0.0005988434 0.9809581329
11 38.6 23 11 24.5 Residual 10 64.8661155357 6.4866115536
12 39.3 24 12 23.5 Total 11 64.87
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
b0 26.505070283 6.3793374833 4.1548311799 0.0019648391 12.2910205864 40.7191199795 12.2910205864 40.7191199795
b1 -0.0046243623 0.1889710296 -0.0244712765 0.9809581329 -0.4256780552 0.4164293306 -0.4256780552 0.4164293306
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 26.3584779976 -2.3584779976
2 26.3802125005 -0.5802125005
3 26.3487668367 4.6512331633
4 26.3663394135 -2.8663394135
5 26.3547785077 2.1452214923
6 26.3501541454 -0.7501541454
Correlation between old and new processes 7 26.3284196425 2.3715803575
-0.0077382654 8 26.3316566961 1.0683433038
9 26.3709637758 2.1290362242
10 26.3603277425 -1.1603277425
11 26.3265698976 -1.8265698976
12 26.323332844 -2.823332844

Process Effect (12 weeks test)

Y 31.7 27 33.799999999999997 30 32.5 33.5 38.200000000000003 37.5 29 31.3 38.6 39.299999999999997 24 25.8 31 23.5 28.5 25.6 28.7 27.4 28.5 25.2 24.5 23.5 Predicted Y 31.7 27 33.799999999999997 30 32.5 33.5 38.200000000000003 37.5 29 31.3 38.6 39.299999999999997 26.358477997577715 26.380212500458764 26.348766836715967 26.366339413513412 26.354778507725619 26.350154145410503 26.32841964252945 26.33165669615003 4 26.370963775828532 26.36032774250376 26.326569897603406 26.323332843982822

Old Process

New Process