residual_diagnostics - Residual Graph Diagnostics Ideal r...

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Unformatted text preview: Residual Graph Diagnostics Ideal: r es i d 2 1 0 - 1 - 2 - 3 0 1 2 3 4 pr ed 5 6 7 8 9 There is no structure here. Ideally we will just get a box with equal amounts of residuals above and below the x axis. Things that can go wrong: r esi d 3 2 1 0 - 1 - 2 - 3 0 1 2 pr ed 3 4 5 Here we have an example of non-constant variance in the residuals. This is the most common form of this issue, where the residuals form a "cone" shape that gets larger as the predicted value gets larger. To correct his problem, we need do a transformation on the dependent variable. r es i d 4 3 2 1 0 - 1 - 2 - 3 - 4 - 1 0 1 2 3 4 5 6 7 pr ed 8 9 10 11 12 13 14 15 16 There are many types of curvi- linear association. Most are easily fixed by doing a polynomial regression, or, if necessary, we can transform the dependent or independent variables. QQ-PLOT Diagnostics An ideal qq plot: 3 2 1 z 0 - 1 - 2 - 3 - 3 - 2 - 1 N o r ma l 0 Qu a n t i l e s 1 2 3 An ideal QQ Plot is a straight line. There should not be too many "wiggles". Note that we have to relax our standards when we have fewer observations. There are also formal tests for normality, however for low sample sizes they are not accurate, and for high sample sizes they are often too stringent to be useful. This one is also normal, but with a smaller sample size: 1. 5 1. 0 0. 5 z 0 - 0. 5 - 1. 0 - 1. 5 - 2 - 1 N o r ma l 0 Qu a n t i l e s 1 2 When sample sizes are smaller, we are less strict in our requirements of linearity. Things that can go wrong: 4 0 - 2. 5 3 - 5. 0 r s 2 l s - 7. 5 - 10. 0 1 - 12. 5 0 - 3 - 2 - 1 N o r ma l 0 Qu a n t i l e s 1 2 3 - 15. 0 - 3 - 2 - 1 N o r ma l 0 Qu a n t i l e s 1 2 3 0. 4 30 20 0. 2 10 0 h t - 10 l t 0 - 20 - 0. 2 - 30 - 40 - 3 - 2 - 1 N o r ma l 0 Qu a n t i l e s 1 2 3 - 0. 4 - 2 - 1 N o r ma l 0 Qu a n t i l e s 1 2 All issues with QQ Plots require transformations of the dependent variable or independent variables. ...
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This note was uploaded on 07/25/2008 for the course STT 422 taught by Professor Porter during the Summer '08 term at Michigan State University.

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residual_diagnostics - Residual Graph Diagnostics Ideal r...

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