attachments_24afa9b267aba3c1c0996f43e085700ba09ce2c4 Year District 82 D2 82 D4 82 D8 84 D1 84 D3 84 D5 84 D7 86 D2 86 D4 86 D8 88 D1 88 D3 88 D5 88 D7 90 D2 90 D4 90 D8 92 D1 92 D3 92 D5 92 D7 93 D2 DemAbsenteeVotes RepubAbsenteeVotes DemMachineVotes RepubMachineVotes 551 205 47767 21340 594 312 44437 28533 338 115 55662 13214 1357 764 58327 38883 716 144 78270 6473 1207 1436 54812 55829 929 258 77136 13730 609 316 39034 23363 666 306 52817 16541 477 171 48315 11605 1101 700 56362 34514 448 70 69801 3939 781 1610 43527 56721 644 250 68702 12602 660 509 27543 26843 482 831 39193 27664 308 148 34598 8551 1923 594 65943 21518 695 327 58480 12968 841 1275 41267 46967 814 423 65516 14310 1396 371 19127 19691 Page 1 qattachments_24afa9b267aba3c1c0996f43e085700ba09ce2c4 DemPctOfAbsenteeVotes DemPctOfMachineVotes Disputed 72.9 69.1 no 65.6 60.9 no 74.6 80.8 no 64 60 no 83.3 92.4 no 45.7 49.5 no 78.3 84.9 no 65.8 62.6 no 68.5 76.2 no 73.6 80.6 no 61.1 62 no 86.5 94.7 no 32.7 43.4 no 72 84.5 no 56.5 50.6 no 36.7 58.6 no 67.5 80.2 no 76.4 75.4 no 68 81.8 no 39.7 46.8 no 65.8 82.1 no 79 49.3 yes Page 2 SUMMARY OUTPUT Regression Statistics Multiple R 0.8720132263 R Square 0.7604070668 Adjusted R Square 0.7477969124 Standard Error 7.4074724987 Observations 21 ANOVA df Regression Residual Total Intercept X Variable 1 SS MS F Significance F 1 3308.764 3308.764 60.30117 2.60E-007 19 1042.542 54.87065 20 4351.307 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% 5.533932996 7.767794 0.71242 0.484862 -10.72425 21.79211 0.8387972426 0.108018 7.765383 2.60E-007 0.612714 1.06488 Lower 95.0% Upper 95.0% -10.72425 21.79211 0.612714 1.06488 SUMMARY OUTPUT Regression Statistics Multiple R 0.872013 R Square 0.760407 Adjusted R 0.747797 Standard E 7.700805 Observatio 21 ANOVA df Regression Residual Total SS MS F Significance F 1 3576.004 3576.004 60.30117 2.60E-007 19 1126.746 59.3024 20 4702.75 CoefficientStandard Et Stat P-value Lower 95%Upper 95%Lower 95. Upper 95.0% Intercept 11.83575 7.718879 1.533351 0.141672 -4.320046 27.99155 -4.320046 27.99155 DemPctOfA0.906545 0.116742 7.765383 2.60E-007 0.662201 1.150888 0.662201 1.150888 Year District 82 D2 82 D4 82 D8 84 D1 84 D3 84 D5 84 D7 86 D2 86 D4 86 D8 88 D1 88 D3 88 D5 88 D7 90 D2 90 D4 90 D8 92 D1 92 D3 92 D5 92 D7 93 D2 DemAbsenteeVotes RepubAbsenteeVotes 551 594 338 1357 716 1207 929 609 666 477 1101 448 781 644 660 482 308 1923 695 841 814 1396 17537 DemMachineVotes 205 47767 312 44437 115 55662 764 58327 144 78270 1436 54812 258 77136 316 39034 306 52817 171 48315 700 56362 70 69801 1610 43527 250 68702 509 27543 831 39193 148 34598 594 65943 327 58480 1275 41267 423 65516 371 19127 RepubMachineVotes DemPctOfAbsenteeVotes DemPctOfMachineVotes Disputed 21340 72.9 69.1 no 28533 65.6 60.9 no 13214 74.6 80.8 no 38883 64 60 no 6473 83.3 92.4 no 55829 45.7 49.5 no 13730 78.3 84.9 no 23363 65.8 62.6 no 16541 68.5 76.2 no 11605 73.6 80.6 no 34514 61.1 62 no 3939 86.5 94.7 no 56721 32.7 43.4 no 12602 72 84.5 no 26843 56.5 50.6 no 27664 36.7 58.6 no 8551 67.5 80.2 no 21518 76.4 75.4 no 12968 68 81.8 no 46967 39.7 46.8 no 14310 65.8 82.1 no 19691 79 49.3 yes Predicted Regression Line DemPctOfMachineVotes 63.5 56.6 73.3 55.9 83.0 47.1 76.7 58.0 69.5 73.1 57.5 85.0 41.9 76.4 48.0 54.7 72.8 68.8 74.1 44.8 74.4 DemPctOfAbsenteeVotes 69.1 72.9 60.9 65.6 80.8 74.6 60 64 92.4 83.3 49.5 45.7 84.9 78.3 62.6 65.8 76.2 68.5 80.6 73.6 62 61.1 94.7 86.5 43.4 32.7 84.5 72 50.6 56.5 58.6 36.7 80.2 67.5 75.4 76.4 81.8 68 46.8 39.7 82.1 65.8 49.3 79 100 90 80 f(x) = 0.71x + 15.72 70 % of Absente Votes 60 50 40 30 20 40 50 60 70 % of Machine Counted Votes 80 90 100 90 80 f(x) = 0.84x + 5.53 70 60 % of Absente Votes 50 40 30 20 40 50 60 70 80 90 % of Machine Counted Votes Question C X value Y value T-value 49.3 46.88663706 2.09302 4 79 71.79891516 2.09302 4 S.E M.E Lower limit Upper Limit 2.767362 5.79215 6 75.1579 8 82.84202 1.83563 67.9569 75.64093 3.84201 7 100 A) Draw a scatterplot of Democratic percentage of absentee ballots versus Democratic percentage of machine-counted ballots. Use a separate plotting symbol to highlight the disputed election. Represented above B) Fit the simple linear regression of absentee percentage on machine-count percentage, excluding the disputed election. Draw this line on the scatter plot. Also, include a 95% prediction band. What does this plot reveal about the unusualness of the absentee percentage In the disputed election? The Disputed value is an outlier. It fails to fit in the regression line and the difference is significant. This is likely to be have been a form of Electro Fraud or abnormally. C) How many estimated standard deviations is the observed absentee percentage, 79.0, from this predicted value? This is about 3.842 standard deviations or approximately 4 standard deviations d. Adjust the p-value with a Bonferroni correction to account for all 22 residuals that could have been similarly considered. ' = 1 - ( 1 - ) k ' = 1 - ( 1 - 0.05 ) 22 The adjusted alpha is thus 0.6765 SUMMARY OUTPUT Regression Statistics Multiple R 0.8720132263 R Square 0.7604070668 Adjusted R Square 0.7477969124 Standard Error 7.4074724987 Observations 21 ANOVA df Regression Residual Total Intercept X Variable 1 SS MS F Significance F 1 3308.764 3308.764 60.30117 2.60E-007 19 1042.542 54.87065 20 4351.307 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% 5.533932996 7.767794 0.71242 0.484862 -10.72425 21.79211 0.8387972426 0.108018 7.765383 2.60E-007 0.612714 1.06488 Lower 95.0% Upper 95.0% -10.72425 21.79211 0.612714 1.06488 SUMMARY OUTPUT Regression Statistics Multiple R 0.872013 R Square 0.760407 Adjusted R 0.747797 Standard E 7.700805 Observatio 21 ANOVA df Regression Residual Total SS MS F Significance F 1 3576.004 3576.004 60.30117 2.60E-007 19 1126.746 59.3024 20 4702.75 CoefficientStandard Et Stat P-value Lower 95%Upper 95%Lower 95. Upper 95.0% Intercept 11.83575 7.718879 1.533351 0.141672 -4.320046 27.99155 -4.320046 27.99155 DemPctOfA0.906545 0.116742 7.765383 2.60E-007 0.662201 1.150888 0.662201 1.150888 Year District 82 D2 82 D4 82 D8 84 D1 84 D3 84 D5 84 D7 86 D2 86 D4 86 D8 88 D1 88 D3 88 D5 88 D7 90 D2 90 D4 90 D8 92 D1 92 D3 92 D5 92 D7 93 D2 DemAbsenteeVotes RepubAbsenteeVotes 551 594 338 1357 716 1207 929 609 666 477 1101 448 781 644 660 482 308 1923 695 841 814 1396 17537 DemMachineVotes 205 47767 312 44437 115 55662 764 58327 144 78270 1436 54812 258 77136 316 39034 306 52817 171 48315 700 56362 70 69801 1610 43527 250 68702 509 27543 831 39193 148 34598 594 65943 327 58480 1275 41267 423 65516 371 19127 RepubMachineVotes DemPctOfAbsenteeVotes DemPctOfMachineVotes Disputed 21340 72.9 69.1 no 28533 65.6 60.9 no 13214 74.6 80.8 no 38883 64 60 no 6473 83.3 92.4 no 55829 45.7 49.5 no 13730 78.3 84.9 no 23363 65.8 62.6 no 16541 68.5 76.2 no 11605 73.6 80.6 no 34514 61.1 62 no 3939 86.5 94.7 no 56721 32.7 43.4 no 12602 72 84.5 no 26843 56.5 50.6 no 27664 36.7 58.6 no 8551 67.5 80.2 no 21518 76.4 75.4 no 12968 68 81.8 no 46967 39.7 46.8 no 14310 65.8 82.1 no 19691 79 49.3 yes Predicted Regression Line DemPctOfMachineVotes 63.5 56.6 73.3 55.9 83.0 47.1 76.7 58.0 69.5 73.1 57.5 85.0 41.9 76.4 48.0 54.7 72.8 68.8 74.1 44.8 74.4 DemPctOfAbsenteeVotes 69.1 72.9 60.9 65.6 80.8 74.6 60 64 92.4 83.3 49.5 45.7 84.9 78.3 62.6 65.8 76.2 68.5 80.6 73.6 62 61.1 94.7 86.5 43.4 32.7 84.5 72 50.6 56.5 58.6 36.7 80.2 67.5 75.4 76.4 81.8 68 46.8 39.7 82.1 65.8 49.3 79 100 90 80 f(x) = 0.71x + 15.72 70 % of Absente Votes 60 50 40 30 20 40 50 60 70 % of Machine Counted Votes 80 90 100 90 80 f(x) = 0.84x + 5.53 70 60 % of Absente Votes 50 40 30 20 40 50 60 70 80 90 % of Machine Counted Votes Question C X value Y value T-value 49.3 46.88663706 2.09302 4 79 71.79891516 2.09302 4 S.E M.E Lower limit Upper Limit 2.767362 5.79215 6 75.1579 8 82.84202 1.83563 67.9569 75.64093 3.84201 7 100 A) Draw a scatterplot of Democratic percentage of absentee ballots versus Democratic percentage of machine-counted ballots. Use a separate plotting symbol to highlight the disputed election. Represented above B) Fit the simple linear regression of absentee percentage on machine-count percentage, excluding the disputed election. Draw this line on the scatter plot. Also, include a 95% prediction band. What does this plot reveal about the unusualness of the absentee percentage In the disputed election? The Disputed value is an outlier. It fails to fit in the regression line and the difference is significant. This is likely to be have been a form of Electro Fraud or abnormally. C) How many estimated standard deviations is the observed absentee percentage, 79.0, from this predicted value? This is about 3.842 standard deviations or approximately 4 standard deviations d. Adjust the p-value with a Bonferroni correction to account for all 22 residuals that could have been similarly considered. ' = 1 - ( 1 - ) k ' = 1 - ( 1 - 0.05 ) 22 The adjusted alpha is thus 0.6765