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# The residuals for dell red are also evenly

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The residuals for dell (red) are also evenly distributed above and below the 0 reference line. The residuals for IBM (green) are also evenly distributed above and below the 0 reference line. The residuals for MAC (blue) are also evenly distributed above and below the 0 reference line. Conclusion: We have captured the information in the categorical variable MAKE. ACTION: Partial F-test REDUCED MODEL: The regression equation is Time2Repair = 69.3 + 3.86 NUMBER + 0.944 NUMBER^2 Predictor Coef SE Coef T P Constant 69.330 8.551 8.11 0.000 NUMBER 3.865 1.271 3.04 0.005 NUMBER^2 0.94393 0.03995 23.63 0.000 S = 14.8567 R-Sq = 99.8% R-Sq(adj) = 99.8% Analysis of Variance Source DF SS MS F P Regression 2 2594595 1297298 5877.56 0.000 Residual Error 27 5959 221 Total 29 2600555 FULL MODEL: The regression equation is Time2Repair = 59.2 + 4.66 NUMBER + 0.921 NUMBER^2 + 23.7 Compac + 6.68 Dell - 18.4 MAC Predictor Coef SE Coef T P

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Constant 59.154 5.764 10.26 0.000 NUMBER 4.6554 0.7450 6.25 0.000 NUMBER^2 0.92096 0.02360 39.03 0.000 Compac 23.650 4.587 5.16 0.000 Dell 6.682 3.857 1.73 0.096 MAC -18.439 5.287 -3.49 0.002 S = 8.04216 R-Sq = 99.9% R-Sq(adj) = 99.9% Analysis of Variance Source DF SS MS F P Regression 5 2599002 519800 8036.95 0.000 Residual Error 24 1552 65 Total 29 2600555 F-ratio = (99.9-99.8)/3 (100-99.9)/24 F-ratio = 8 Critical F-value: (0.05, 3, 24) =FINV(alpha, dfnum, dfnom) = FINV(0.05, 3, 24) = 3.00878 Conclusion: the F-ratio (8) is larger than the critical F value therefore the increase in R^2 is statistically significant. VALIDATION: Range: stnd Residual: Residual 14.00035 1.862649 Range = -14 minutes to 14 minutes TEST OBSERVATION: Time2Repair = 525 NUMBER = 20 MAKE = Dell Time2Repair = 59.2 + 4.66 NUMBER + 0.921 NUMBER^2 + 23.7 Compac + 6.68 Dell - 18.4 MAC Time2Repair = 59.2 + 4.66(20) + .921 (400) + 23.7(0) + 6.68(1) – 18.4(0) Time2repair = 527.48 Ei = actual – predicted Ei = 525 – 527.48 Ei = -2.48 Conclusion: Because the residual of the test observation falls in the test range, We are able to validate the model for use with current data. Reccomendation: We recommend the use of the new model to predict Time2repair. 1. R 2 is valid and its 99.9% 2. The partial F-test shows that the increase in R 2 is statistically significant. 3. The model is validated for use with new data 4. NUMBER expressed as polynomial is statistically related to Time2repair.
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