Lec10.MultiReg

Lec10.MultiReg - Multiple Regression KNNL Chapter 6 6.1...

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Unformatted text preview: Multiple Regression KNNL Chapter 6 6.1 Intro 6.2 Matrix 6.5 ANOVA 6.6 Parameters 6.7 Mean Response 6.8 Diagnostics 6.9 Example Multiple Predictors Single Response ε Xβ Y + = + + = + + + + + = ∑- = i p k ki k i i i i i i i x y x x x x y ε β β ε β β β β β 1 1 4 4 3 3 2 2 1 1 Coal-Ash Data Robena Mine, Greene County, PA Gomez and Hazen (1970) Cressie (1993) Percent coal-ash 208 coal-ash cores 2500 ft spacing Coal-Ash Data (coal.ash.txt) coal.ash x y coal 1 1 14 10.21 2 1 15 9.92 3 1 16 11.17 4 2 8 10.01 5 2 10 11.15 6 2 11 11.31 7 2 12 9.92 8 2 14 10.73 9 2 15 10.82 10 2 16 10.14 x y 5 10 15 5 10 15 20 y vs. x Percent Coal Ash x y 5 10 15 5 10 15 20 10.21 9.92 11.17 10.01 11.15 11.31 9.92 10.73 10.82 10.14 9.97 9.93 11.65 9.46 12.5 11.05 9.41 9.91 10.82 8.23 10.39 10.41 9.76 10.93 9.79 10.74 11.21 9.7 10.27 8.96 9.35 9.63 10.11 9.37 10.17 11.75 11.04 11.11 10.82 11.1 10.94 9.64 9.29 10.59 10.43 8.75 9.52 9.53 10.8 17.61 10.96 10.28 9.78 10.55 11.21 11.46 10.82 9.78 9.88 10.21 9.84 9.89 12.8 9.06 10.39 9.32 8.96 10.06 10.61 8.86 10.87 10.83 13.07 11 11.61 9.93 10.41 10.12 10.38 8.9 11.09 10.29 10.34 10.03 10.7 10.65 8.27 12.65 10.27 9.48 10.09 10.47 9.79 9.16 10.7 8.45 9.4 9.79 10.18 10.63 9.84 8.2 9.36 11.21 10.36 11.62 8.14 9.63 9.59 9.22 13.06 8.69 11.58 10.19 10.04 9.27 8.9 9.48 8.91 9.34 8.82 10.01 9.82 8.57 8.98 9.58 10.91 9.82 9.61 11.41 11.17 9.46 9.15 11.19 9.28 8.07 10.99 9.22 10.56 10.18 9.01 10.06 9.01 9.27 10.66 8.76 7.81 8.2 9.96 9.39 8.54 8.15 8.1 10.13 7.96 9.92 11.43 9.06 9.34 7.68 8.58 9.04 8.19 8.92 8.89 8.59 9.15 9.56 10.87 9.2 11.3 8.61 7 7.85 8.61 9.25 8.89 7.28 7.88 7.8 9.1 9 8.78 7.9 8.21 7.83 8.64 9.58 7.61 7.84 7.62 11.86 9.14 7.04 9.69 8.2 9.03 9.65 8.91 8.81 9.96 8.77 8.6 9.99 7.63 7.95 9.91 9.07 X-5 5 10 15 20 5 10 15 20 Y Percent Coal Ash 8 10 12 14 16 18 x coal 5 10 15 8 10 12 14 16 18 coal vs. x y coal 5 10 15 20 8 10 12 14 16 18 coal vs. y Multiple Regression on Coal Ash error NS EW Intercept l PercentCoa x x y i i i i + + + = + + + = ε β β β 2 2 1 1 Splus Linear Model coal.lm = lm(coal~x+y,data=coal.ash) # summary(coal.lm) Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) 11.2468 0.2250 49.9818 0.0000 x -0.1771 0.0252 -7.0332 0.0000 y -0.0104 0.0141 -0.7368 0.4621 x coal 5 10 15 8 10 12 14 16 18 coal vs. x i i x y 1 1 ˆ β β + = y coal 5 10 15 20 8 10 12 14 16 18 coal vs. y i i x y 2 2 ˆ β β + = coal vs. x and y Higher Order Effects...
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This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell.

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Lec10.MultiReg - Multiple Regression KNNL Chapter 6 6.1...

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