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Direction: The Invisible Player

Direction: The Invisible Player. Robert E. Johnson Dept. of Mathematical Sciences VCU Based on - Johnson and Herr, “Direction: The Invisible Player”, ASA Proceedings of the Statistical Education Section, 48-52, 1993. Workload Related to Anesthesiology Service. Dependent Variable

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Direction: The Invisible Player

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  1. Direction:The Invisible Player Robert E. Johnson Dept. of Mathematical Sciences VCU Based on - Johnson and Herr, “Direction: The Invisible Player”, ASA Proceedings of the Statistical Education Section, 48-52, 1993.

  2. Workload Related to Anesthesiology Service • Dependent Variable • WORKLOAD: man-hours • Independent Variables • CASES: number of surgical cases • ELIGIBLE: rate of service eligibility per 1000 patients Source: Procedures and Analyses for Staffing Standards Development: Data/Regression Analysis Handbook. San Diego, CA: Navy Manpower and Material Analysis Center, 1979. [From: Myers, Classical and Modern Regression with Applications, PWS-Kent Publishing Co., Boston, MA, 1990 (pages 381-383)].

  3. CorrelationsWorkload/Anesthesiology Service • Cases Eligible • Workload 0.9800.971 • (<0.001) (<0.001)

  4. Regression AnalysisWorkload/Anesthesiology Service • Analysis of Variance Section • Sum of Mean Prob • Source DF Squares Square F-Ratio Level • Model 2 1.457E+07 7284372.7 124.752<0.001 • Error 9 525517.4 58390.82 • Total(Adj.) 11 1.509E+07 • Root Mean Square Error 241.642 R-Squared 0.965

  5. Regression AnalysisWorkload/Anesthesiology Service • Regression Equation Section • Indep. Regression Standard T-Value Prob • Variable Coefficient Error (Ho: B=0) Level • Intercept 137.2353 115.0564 1.193 0.264 • Cases 2.960778 1.214657 2.438 0.038 • Eligible 3.085881 2.919934 1.057 0.318

  6. CorrelationsWorkload/Anesthesiology Service • Cases Eligible • Workload 0.9800.971 • (<0.001) (<0.001) • Cases 0.975 • (<0.001)

  7. X=Cases; Z=Eligible; Y=Workload

  8. Growth Rate in Experimental Rats • Dependent Variable • GROWTH: growth rate • Independent Variables • DOSE: dosage of a dietary supplement • DOSESQ: dosage squared Hypothetical Data Source: SAS Institute Inc., SAS/STAT User’s Guide, Version 6, Fourth Edition, Volume 2, SAS Institute Inc., Cary, NC, 1989 (page 1438).

  9. CorrelationsGrowth Rate in Experimental Rats • Dose DoseSq • Growth .186.359(0.608) (0.309)

  10. Regression AnalysisGrowth Rate in Experimental Rats • Analysis of Variance Section • Sum of Mean Prob • Source DF Squares Square F-Ratio Level • Model 2 655.706 332.853 51.555<0.001 • Error 7 45.1938 6.45626 • Total(Adj.) 9 710.9 78.9889 • Root Mean Square Error 2.541 R-Squared 0.936

  11. Regression AnalysisGrowth Rate in Experimental Rats • Regression Equation Section • Indep. Regression Standard T-Value Prob • Variable Coefficient Error (Ho: B=0) Level • Intercept 35.65744 5.617927 6.34714E-04 • Dose 5.262896 0.558022 9.43133E-05 • DoseSq 0.12767 0.012811 9.9662E-05

  12. CorrelationsGrowth Rate in Experimental Rats • Dose DoseSq • Growth .186.359(0.608) (0.309) • Dose 0.983 • (<0.001)

  13. X=Dose; Z=DoseSq; Y=Growth

  14. Unique Contribution of an Independent Variableto the Total Variation (CSS) “When independent variables are correlated, there is no unique sum of squares which can be ascribed to an independent variable as reflecting its effect in reducing the total variation in Y. The reduction in total variation ascribed to an independent variable must be viewed in the context of the other independent variables in the model…” - Neter & Wasserman Neter and Wasserman, Applied Linear Statistical Models,Richard D. Irwin, Inc., 1974 (page 253).

  15. Contribution of an Independent Variableto the Total Variation (CSS) Type 3: Partial SSThe SS ascribed to the direction in the XZc-plane orthogonal to X. This is the reduction in error SS when Z joins X in the model. Type 1 SSThe SS ascribed to the direction of Z. This is the regression SS when Z is the only variable in the model.

  16. Contribution of an Independent Variableto the Total Variation (CSS)

  17. Contribution of an Independent Variableto the Total Variation (CSS) W XZc-plane

  18. Contribution of an Independent Variableto the Total Variation (CSS) W XZc-plane Given Xc and the XZc-plane, there is no unique direction in the plane which can be ascribed to this SS.

  19. Variance Inflation Factor (VIF)

  20. a b Variance Inflation Factor (VIF)

  21. VIF: Variance Inflation Factor

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