Topic 05 - Topic 5 Partial Correlations; Diagnostics &...

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1 Topic 5 – Partial Correlations; Diagnostics & Remedial Measures Chapters 10 & 14
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2 Overview Review: Partial Correlations – Think “Extra” SS being used to compute “Extra” R 2 Of the variation left to explain. ..How much is explained by adding another group of variables? We’ve already talked a lot about this. So. ..some review, with a few additional points to be made.
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3 Review (Tests) 1. ANOVA F Test : Does the group of predictor variables explain a significant percentage of the variation in the response? 2. Variable Added Last T-tests : Does a given variable explain a significant part of the variation remaining after all other variables have been included in the model? 3. Partial F Tests : Does a group of variables explain significant variation in the response over and above that already explained by other variables already in the model?
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4 Review (ESS) Extra Sums of Squares is SS due to the added group of variables over and above any variables (given) already in the model. For Example: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 1 1 2 3 1 1 2 3 1 | , , | , , SS X X SS X X SS X SS X X X SS X X X SS X = - = -
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5 Review SS(X1) SS(X3|X1,X2) Total SS SS(X2|X1)
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6 Review (SAS) Type I SS is sequential sums of squares: Type II (or III) SS is extra sums of squares for variables added last: For X2, ( 29 ( 29 ( 29 ( 29 1 2 1 3 1 2 4 1 2 3 | | , | , , ... SS X SS X X SS X X X SS X X X X ( 29 2 1 3 4 | , , , SS X X X X etc
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7 Review (ESS) Type I SS are additive and sum to SSR. If the variables are added in the proper order, any ESS may be computed using the Type I sums of squares. Type II SS are not additive and can only be used to assess the contribution of an individual variable over and above the rest of the predictors in the model. In a lot of ways, the Type II SS are giving the same information that variable added last t-tests gave. The presentation is in SS instead of sig. tests.
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8 Review (General Linear Test) The test is performed by comparing variances between the full and reduced models. F-statistic is based on SS: ( 29 ( 29 ( 29 This is EXTRA SS for the added variables / SSE reduced SSE full k F MSE full - = 6 4 4 4 447 4 4 4 4 48
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9 Review: Hypotheses Test comparing two models (null model subset of full model): Above is same as Rejecting means at least one variable in the “added group” is important. 0 0 1 1 0 1 1 2 2 3 3 : : i a i H Y X H Y X X X β ε = + + = + + + + 0 2 3 : 0 H = =
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10 Correlations: Multiple, Partial Using Multiple & Partial Correlations in Multiple Regression Analysis (Chapter 10)
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Review (R 2 ) R 2 is called the coefficient of determination Computationally: Conceptually: describes the percentage of the total sums of squares that is in fact explained by the predictor variables. 2
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This note was uploaded on 02/20/2012 for the course STAT 502 taught by Professor Staff during the Fall '08 term at Purdue.

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Topic 05 - Topic 5 Partial Correlations; Diagnostics &...

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