class (Y) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AFP 5.15 3.2 6.71 1.4 2.73 4.75 4.89 1.18 8.38 3.87 5.93 9.18 2.54 6.11 1.61 3.18 3.04 2.9 5.33 1.01 1.76 3.1 3.99 1.139 7.24 6.98 6.66 7.58 6.72 1.842 4.79 2.286 4.43 4.73 6.27 2.91 7.87 2.44 1 13.7 6.16 6.19 5.65 3.39 4 3.97 CEA CA125 CA199 10.4 8.24 21.62 4.7 6.55 5.81 45.8 1.41 0.75 2.6 6.09 3.98 1.8 17.34 3.94 2.7 5 6.77 1.8 10.71 1.06 0.9 7.93 1.53 0.6 0.33 5.98 21.3 15.54 0 8.9 1.48 38.3 5.5 5.49 40.37 1.7 5.68 22.54 13.5 9.15 19.18 1.4 4.81 4.59 1.3 5.78 4.42 20.5 28.35 22.72 29.2 9.39 32.72 8.9 8.44 5.03 1.5 2.25 1.74 6.9 5.98 8.61 14.1 6.26 21.88 3.5 8.55 5.99 16.8 10.09 147.84 2.6 8.04 1.69 7.7 7.3 10.11 1.9 2.94 38.12 3.1 15.14 19.19 6.2 4.97 9.19 0.4 9.44 2.33 9.2 2.2 1.69 1.2 6.13 3.61 7.9 31.3 0 8.3 11.06 218.91 19.2 8.16 13.5 2.2 5.94 4.59 4.5 5.91 12.71 3.6 3.27 10.45 10.3 6.42 16.24 4.5 4.2 2.55 1.9 11.83 75.8 5 4.08 8.5 4.9 5.85 11.23 5 6.89 0 7.9 3.75 92.6 1.4 2.69 5.02 CA50 54.29 13.69 7.21 14.62 8.15 11.61 7.34 4.75 10.4 7.89 22.75 27.88 21.57 18.85 9.34 7.17 17.95 29.49 15.32 14.46 12.3 18.94 7.07 54.47 6.31 10.45 33.51 21.17 15.13 13.97 5.99 13.25 7.33 72.54 22.01 6 13.53 13.22 14.93 5.83 28.35 24.95 9.27 7.83 65.84 8.59 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9.61 0.339 4.7 7.47 4.11 3.5 1.07 3.51 5.28 4 2.1 6.62 3.42 5.54 1.23 11.81 1.482 7.87 4.38 2.2 4.51 2.53 3.81 3.81 2.1 3.2 6.11 3.7 6.62 1.04 0.6 3.86 4.12 6.23 1 6.09 2.13 3.67 3.96 2.96 5.24 5.9 1.1 5.59 6.4 4.93 3.9 54.2 5 37.5 2.8 2.8 1.2 24 84.8 25.4 4.7 1.5 6 3.5 13.2 18.9 17.9 4.9 1.5 1.4 3.3 1.2 180 5.2 5.2 3.7 2.4 11.5 3 36.9 1.7 21.1 0.9 1.6 1.2 19.1 5.4 2.4 7.6 5.1 2.1 1.7 29.1 17.6 0.7 3.5 0.7 1 12.8 4.58 19.79 4.05 10.62 2.94 8.72 7.18 5.41 3.47 7.36 2.69 8.07 32.85 3.6 6.42 8.13 4.64 6.42 11.92 77.46 10.07 7.78 7.78 10.88 9.81 5.11 64.84 7.17 10.17 30.9 1.96 8.8 2.7 4.24 27.14 5.69 3.48 5.94 4.81 5.83 8.52 10.16 8.34 7.67 5.05 2.77 104.04 9.97 32.28 1.55 15.18 3.51 0 23.95 0 26.79 17.8 7.07 10.06 40.29 6.79 0 8.39 0.46 10.32 10.46 23.5 33.77 15.63 15.63 26.38 10.81 44.62 23.02 67.21 0.06 20.8 2.7 8.04 7.27 8.42 46.48 6.98 0 5.69 4.79 38.89 6.37 14.45 2.96 17.09 4.87 16.47 159.49 13.71 27.38 11.15 12.1 7.79 4.79 21.27 2.4 19.06 27.6 13.71 12.6 8.3 9.59 10.13 16.42 14.12 14.01 15.75 14.5 22.3 9.74 9.74 22.89 12.93 25.82 28.81 31.8 6.56 17.18 7.12 16.36 10 16.02 24.67 7.08 4.12 8.35 16.9 23.84 12.98 22.09 15.9 16.03 12.35 18.7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.22 6.62 2.14 0.9 2.637 3.4 2.55 5.29 1.85 2.54 4.3 3.05 4.01 5.58 82.26 5.93 1.84 4.25 1.2 1.9 3.8 5.95 5.45 3.11 5.91 6.19 2.7 1.4 3.05 2.8 1.4 6.3 1.63 5.37 4.87 4.89 3.23 3.3 7.49 5.2 4.12 9.16 3.28 2.89 8.74 5.32 1.87 1.5 1.3 2.2 2 2 0.9 7.4 1.9 2.1 13.4 2.2 1.8 0.9 33.4 1.7 1.3 25 1.9 1.1 0.4 3.2 0.8 0.5 1.4 1.4 1 0.7 1.6 5.9 2 0.8 1.4 1.6 1.4 0.5 1.8 7.1 1.8 1.3 1.6 0.8 1.4 1.1 1.2 0.8 0.5 0.3 6.15 12.5 3.96 2.02 13.27 4.65 4.4 5.63 14.45 4.15 12.23 5.95 19.02 3.54 5.7 5.15 8.3 5.07 3.62 8.71 9.53 11.64 7.09 1.35 109 12.56 0.3 13.94 14.59 3.2 34.08 6.22 4.04 7.75 3.9 10.71 5.53 13.08 3.49 264.41 3.95 3.94 0.74 6.16 3.42 6.14 8.47 4.16 3.24 6.3 32.16 11.48 13.22 8.58 152.32 7.86 2.79 4.39 2.96 17.77 15.38 99.71 13.14 11.54 1.7 0.3 2.15 12.12 8.49 1.27 16.06 14.08 32.93 0.3 4.98 12.01 1.22 4.35 0.5 13.03 8.81 2.74 1.06 28.13 2.62 5.33 15.36 3.99 21.86 3.32 8.6 8.08 6.3 2.65 8.78 25.35 10.28 42.37 14.26 20.05 1.68 61.18 8.48 7.02 13.26 6.37 16.55 24.24 52.14 12.66 9.93 10.68 3.17 4.53 9.9 10.76 6.13 19.66 13.2 16.37 3.13 14.39 13.35 9.37 9.3 3.93 10.26 11.28 13.1 7.34 14.04 9.06 10.1 10.44 10.87 9.23 6.78 13.28 11.9 10.24 9.89 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.27 9.06 4.2 3.81 4.13 9.18 3.08 2.3 1.4 5.73 2.03 1.27 3.3 0.76 9.11 1.4 9.96 13.76 3.83 1.38 1 6.1 3.98 10.48 1.94 2.9 8.03 0.6 0.9 15.25 2.06 4.64 5.2 1.91 1.1 3.49 2.95 2.1 5.22 0.99 2.27 6 6.38 3.64 2.25 2.5 2.9 1.4 6.1 1.9 1.2 0.3 5.5 1.1 2.5 1.8 2.4 4.5 0.5 2.1 0.3 2.6 2.6 0.5 1.1 1.2 1.9 1.4 4.9 0.5 1.4 6.6 1.2 2.8 0.3 1.1 0.5 0.9 0.4 2.7 1.6 0.3 0.4 0.9 11.8 1.7 0.6 2.3 0.9 0.9 1.5 1.1 2.3 2 8.24 4.12 4.8 14.21 4.96 5.49 4.58 6.14 7.83 9.62 8.9 3.62 5.49 3.2 6.4 6.09 1.39 5.78 4.2 3.69 59.4 5.08 8.17 5.07 5.22 6.9 219.66 2.82 6.82 5.23 7.35 0.84 14 4.4 27.53 9.35 5.02 15.51 5.82 10.09 13.52 6.14 12 5.99 9.72 6.54 7.48 37.3 36.36 4.94 0 5.01 40.37 6.12 1.94 4.35 12.56 48.3 1.06 0.09 2.99 13.39 3.98 2.37 3.43 4.75 1.4 5.28 1.38 0.18 20.54 0 7.38 0 0.99 9.7 9.97 2.23 3.09 20.49 14.5 2.88 2.92 5.12 196.92 0 3.35 2.72 4.06 14.09 0 12.22 0.02 1.72 21.35 26.96 16.43 8.71 13.43 27.88 7.46 8.07 11.15 17.58 21.67 9.71 2.67 6.8 16.63 14.62 10.98 11.5 6.57 5.89 9.6 9.04 8.11 72.63 5.53 11.28 4.74 4.9 24.11 15.75 4.5 10.63 11.1 13.79 60.51 8.61 7.06 52.14 11.49 14.88 5.56 8.8 17.24 2.56 17.27 5.27 4.94 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5.7 4.559 1.3 2.3 4.68 2.6 4.61 4.77 1.3 1.6 2.8 3.59 1.62 6.24 6.17 1.3 5.24 4.09 1.4 5.72 6.16 6.86 7.17 2.9 5.59 4.15 2.9 3.59 11.5 4.66 6.59 9.92 1.4 10.22 7.96 9.7 8.42 1.6 3.34 7.9 2.52 1.4 5.52 1.7 1.01 2.78 1.7 1.5 1.9 1.7 5.7 0.6 1.9 1.9 1.8 1.2 0.6 1.8 1.9 1.7 3 1.5 2.5 1.9 2 1.1 0.5 0.6 0.2 0.8 0.5 3 1.6 0.3 0.5 3 1.2 1.4 13.8 0.6 3.1 1.5 1.1 4 4 6.1 1.8 1.8 0.8 0.8 1.4 0.6 2.9 12.92 2.28 6.94 7.02 7.11 9.76 5.41 8.11 2.45 17.12 13.41 9.82 33.97 2.26 3.95 8.83 0.1 10.06 13.03 0.01 4.6 45.64 4.17 4.66 2.82 3.67 7.54 4.49 13.3 5.93 1.97 6.5 44.44 6.95 10.62 4.59 17.53 7.31 5.06 75.47 0 7.14 8.19 5.72 1.33 3.32 7.21 22.06 4.32 12.14 18.7 20.41 23.76 5.77 6.77 6.26 6.14 1.56 10.03 0 2.13 16.51 1.44 0.3 25.61 48.13 4.54 5.73 9.8 3.17 21.46 1.27 12.58 5.22 8.44 1.15 6.71 3.16 4.84 45.38 2.17 8.64 6.94 0.14 12.5 36.96 64.12 26.21 13.48 2.36 4.28 4.39 1.56 18.04 18.72 14.95 16.52 12.76 26.07 23.94 16.44 13.17 10.72 8.27 12.29 14.25 3.56 7.85 14.83 10.65 2.25 19.91 24.97 9.91 11.04 13.91 7.3 29.22 20.24 14.94 13.51 17.74 5.75 10.91 7.8 8.6 25.09 7.89 12.42 12.61 3.93 16.48 31.09 40.21 26.52 18.75 7.59 9.1 11.26 8.3 14.63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.81 3 5.58 4.5 2.29 2 1.6 2.55 3.52 1.1 6.44 2.17 5.92 5.24 7.94 2.7 6.42 3.24 6.8 7.5 1.3 1.2 3 33.4 2.3 2 1.5 1.1 0.3 1.5 0.8 1.3 1 0.9 24.6 1.2 1.2 2.2 1.4 0.7 1.2 0.5 279.49 12.7 3.54 4.63 5.53 10.36 7.94 21.77 3.91 2.34 8.29 27.25 7.45 316.92 11.04 6.36 7.28 9.88 50.27 5.26 5.63 25.48 5.88 15.38 3.24 1.58 10.39 0.6 5.69 2.89 5.54 17.96 10.18 4.82 0 1.35 2.16 2.71 30.54 1.71 13.13 5.84 15.14 13.32 24.24 7.67 6.76 16.49 4.78 7.86 12.3 9.18 41.29 11.11 12.45 7.06 8.27 7.97 15.08 27.51 5.65 16.94 13.98 Develop a logistic regression for the provided dataset, where, in addition to CEA, four other commonly used biomarkers for Colorectal Cancer diagnosis and screening are also provided. 1. Build a logistic Regression Model that uses all five independent variables with the Excel Logistic Regression Add-in. 2. Use the excel output and p-values to determine which of the slopes are contributing significantly to the model (alpha=0.05); Remove those independent variables whose slopes are not significant, and build another logistic regression model using the remaining independent variables. Let us call it the final model. 3. Interpret the meaning of the slopes remaining in the final model. 4. Use the excel sheet (m9_logit/Performance on CEA) provided as a template to produce the performance measures and the associated graphs for the final model. (Make sure you understand what the excel sheet does. Not just blindly copy and paste!) 5. What is the maximum accuracy that can be achieved by the final model? 6. What is the associated cut-off value in terms of predicted probability? 7. How would you diagnose this new patient with the final model and the selected optimal cut-off point? AFP CEA C A125 CA199 CA50 5.15 74.4 32.24 21.62 54.29