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Multivariate Linear Regression

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Presentation Transcript

  1. Multivariate Linear Regression

  2. Multiple Regression with a Single Response and r Predictors

  3. Least Squares Estimation (No Linear Dependencies among Predictors)

  4. Sums of Squares Decomposition

  5. Geometry of Least Squares

  6. Least Squares Estimators – Sampling Properties - I

  7. Least Squares Estimators – Sampling Properties - II

  8. Gauss’ Theorem

  9. Inferences Based on Normality of Errors - I

  10. Inferences Based on Normality of Errors - II

  11. Estimating the Mean and Predicting New Observations

  12. Multivariate Multiple Regression – m Response Variables

  13. Least Squares Estimation and Sums of Squares and Cross-Products

  14. Predicted Values, Residuals, and SSCP Matrices

  15. Mean and Variance/Covariance Structure of Least Squares Estimator

  16. Properties of Residuals and SSCPERROR Matrix

  17. Covariance of Regression Coefficients and Residuals

  18. Estimating Mean Responses and Forecasting New Responses at z0

  19. Model with Normal Distribution for Errors

  20. Likelihood Ratio Tests for Regression Coefficients

  21. Alternative Test Statistics

  22. Multivariate Multiple Regression Tests - I

  23. Multivariate Multiple Regression Tests - II

  24. Inference Regarding Predictions

  25. Classical Regression Model – Univariate Response

  26. Classical Regression Model – Univariate Response - Estimators

  27. Classical Regression Model – Multivariate Response

  28. Predictions and Partial Correlation Coefficients

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