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Multiple Linear Regression

Multiple Linear Regression. (MLR). Testing the additional contribution made by adding an independent variable. Predicting SALARY using YRSRANK. Predicting SALARY using YRSRANK. SST = SSY = variation in SALARY. Predicting SALARY using YRSRANK. SST = SSY = variation in SALARY.

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Multiple Linear Regression

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  1. Multiple Linear Regression (MLR) Testing the additional contribution made by adding an independent variable.

  2. Predicting SALARY using YRSRANK

  3. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY

  4. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY

  5. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697

  6. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression

  7. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR = 117,824,722

  8. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR = 117,824,722 R Square = SSR/SST ≈ .1167 or 11.67%

  9. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR = 117,824,722 R Square = SSR/SST ≈ .1167 or 11.67%

  10. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 Adding RANK as a second independent variable will explain more of the variation in SALARY, but will it be a significant amount? SSR = variation explained by regression SSR = 117,824,722 R Square = SSR/SST ≈ .1167 or 11.67%

  11. Predicting SALARY using RANK and YRSRANK

  12. Predicting SALARY using RANK and YRSRANK

  13. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY

  14. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY

  15. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697

  16. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression

  17. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR(RANK and YRSRANK) = 683,715,472.1

  18. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR(RANK and YRSRANK) = 683,715,472.1 R Square = SSR/SST ≈ .6774 or 67.74%

  19. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR(RANK and YRSRANK) = 683,715,472.1 R Square = SSR/SST ≈ .6774 or 67.74%

  20. Predicting SALARY using YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 Adding RANK as a second independent variable will explain more of the variation in SALARY, but will it be a significant amount? SSR = variation explained by regression SSR (YRSRANK) = 117,824,722 R Square = SSR/SST ≈ .1167 or 11.67%

  21. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 SSR = variation explained by regression SSR(RANK and YRSRANK) = 683,715,472.1 R Square = SSR/SST ≈ .6774 or 67.74% SSR (YRSRANK) = 117,824,722

  22. Predicting SALARY using RANK and YRSRANK SST = SSY = variation in SALARY variation in SALARY= 1,009,361,697 We may determine if this additional contribution is significant by performing a partial F-test. SSR = variation explained by regression SSR(RANK and YRSRANK) = 683,715,472.1 R Square = SSR/SST ≈ .6774 or 67.74% Additionalcontribution made by adding RANK = SSR(RANK | YRSRANK) = 683,715,472.1 - 117,824,722 = 565,890,750.1 SSR (YRSRANK) = 117,824,722

  23. Partial F-test (α = .05) Additionalcontribution made by adding RANK = SSR(RANK | YRSRANK) = 683,715,472.1 - 117,824,722 = 565,890,750.1, the numerator.

  24. Predicting SALARY using RANK and YRSRANK

  25. Predicting SALARY using RANK and YRSRANK

  26. Partial F-test (α = .05) In Simple Linear Regression, what was the relationship between the F-test and the t-test? The square root of the F ≈ 9.5969, the t value for RANK.

  27. Predicting SALARY using RANK and YRSRANK The partial F-test and the t-test are equivalent, provided that one is examining the additional contribution of a single independent variable.

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