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Example_Outliers_data_pairs

# Example_Outliers_data_pairs - Example data for outliers...

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J. M. Cimbala This example is done as an in-class example. i x y Y zero line 1 0 3.7 4.81 1.11 0.26 0 2 0.1 4.2 5.52 1.32 0.31 0 3 0.2 5.1 6.22 1.12 0.26 0 4 0.3 6.6 6.93 0.33 0.08 0 5 0.4 7.4 7.63 0.23 0.05 0 6 0.5 8.9 8.34 -0.56 -0.13 0 7 0.6 10.4 9.04 -1.36 -0.32 0 8 0.7 10.9 9.75 -1.15 -0.27 0 9 0.8 11.9 10.45 -1.45 -0.34 0 10 0.9 11.5 11.16 -0.34 -0.08 0 11 1 12.2 11.86 -0.34 -0.08 0 12 1.1 14.7 12.57 -2.13 -0.5 0 13 1.2 15.3 13.27 -2.03 -0.48 0 14 1.3 16.8 13.98 -2.82 -0.66 0 15 1.4 17.2 14.68 -2.52 -0.59 0 16 1.5 5.6 15.39 9.79 2.3 0 17 1.6 19.5 16.09 -3.41 -0.8 0 18 1.7 4.5 16.8 12.3 2.9 0 19 1.8 21.3 17.5 -3.8 -0.89 0 20 1.9 22.5 18.21 -4.29 -1.01 0 Perform a regression analysis to calculate the best-fit straight line through the data: SUMMARY OUTPUT Regression Statistics Multiple R 0.71 R Square 0.5 Adjusted R Square 0.48 Standard Error 4.25 Observations 20 ANOVA df SS MS F Significance F Regression 1 330.35 330.35 18.32 0 Residual 18 324.65 18.04 Total 19 655 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% Intercept 4.81 1.83 2.63 0.02 0.97 8.66 0.97 8.66 X Variable 1 7.05 1.65 4.28 0 3.59 10.51 3.59 10.51 Plot of the data and the curve fit, and plot of the standardized residuals: Example data for outliers in ( x , y ) data pairs e i = Y i - y i e i / S y,x ( Data Analysis -Regression ) 5 10 15 20 25 Column C Column D y -1 0 1 2 3 Column F Column G ei / Sy,x

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= 2.9 > 2 and this standardized residual is not consistent with its neighbors. so This data point is indeed an outlier. Round 2 - re-do the analysis, but with the outlier removed. [We can only remove one outlier at a time.] i x y Y zero line 1 0 3.7 4 0.3 0.1 0 2 0.1 4.2 4.87 0.67 0.22 0 3 0.2 5.1 5.73 0.63 0.21 0 4 0.3 6.6 6.6 0 0 0 5 0.4 7.4 7.46 0.06 0.02 0 6 0.5 8.9 8.33 -0.57 -0.19 0 7 0.6 10.4 9.19 -1.21 -0.41 0 8 0.7 10.9 10.06 -0.84 -0.28 0 9 0.8 11.9 10.92 -0.98 -0.33 0 10 0.9 11.5 11.79 0.29 0.1 0 11 1 12.2 12.65 0.45 0.15 0 12 1.1 14.7 13.52 -1.18 -0.4 0 13 1.2 15.3 14.38 -0.92 -0.31 0 14 1.3 16.8 15.25 -1.55 -0.52 0 15 1.4 17.2 16.11 -1.09 -0.37 0 16 1.5 5.6 16.98 11.38 3.83 0 17 1.6 19.5 17.84 -1.66 -0.56 0 19 1.8 21.3 19.57 -1.73 -0.58 0 20 1.9 22.5 20.44 -2.06 -0.69 0 Perform a regression analysis to calculate the best-fit straight line through the data: SUMMARY OUTPUT Regression Statistics Multiple R 0.87 R Square 0.75 Adjusted R Square 0.74 Standard Error 2.97 Observations 19 ANOVA df SS MS F Significance F Regression 1 453.33 453.33 51.4 0 Residual 17 149.95 8.82 Total 18 603.27 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% Intercept
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