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Lecture 18 2010

# Lecture 18 2010 - IV Multiple Regression A Introduction B...

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1 IV. Multiple Regression . A. Introduction B. CRM C. Estimation D. Interpretation of Parameter Estimates E. Properties of Estimators. F. Estimator for σ 2 and Variances for G. Inferences in Multiple Regression H. Goodness of Fit I. Analysis of Variance ˆ s β H. Goodness of Fit – R 2 1. Multiple Coefficient of Determination – R 2 2. Calculation – exactly the same. R 2 = ESS / TSS = 1 – (RSS / TSS) 3 Adjusted R 2 : 3. Adjusted R : 2 1 1 1 RSS n R TSS n K = R 2 – used for assessing how well a model fits. Adj. R 2 – used to compare two models . Same sample – same Y values. I. Analysis of Variance – F tests. 1. Introduction: R 2 – measures how much variation is explained by the regression. Suppose R 2 = 0.12. The regression l f h explains 12% of the variation in Y. Is 12% a significant portion of the variation in Y? F tests : statistical tests that determine whether the amount of variation explained is statistically significant.

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