multipleRegressionLabSolutions

multipleRegressionLabSolutions - Homework#8 Multiple Linear...

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Unformatted text preview: Homework #8: Multiple Linear Regression — solutions OR&IE 3120, Spring 2009 Problem 1 (a) The last column of the scatterplot matrix has plots of BatchTime against the predictors. Clearly, GateDiam affects BatchTime . No other predictor has an obvious effect on BatchTime . The plots in the other columns beside the last are not relevant for answering this question, but are useful in showing a lack of correlation (good) between the predictors. (b) The relationship between GateDiam and BatchTime appears nonlinear, since there is some curvature in the plot of these two variables. GateDiam 4.0 5.0 6.0 5.5 7.0 0.4 1.0 2.5 3.5 3400 4200 0.2 0.6 4.05.06.0 CupHeight SprueHeight 9.0 11.0 5.5 7.0 RiserDiam SprueDiamBot 0.30.6 0.4 1.0 SprueDiamTop RiserHeight 3.5 5.0 2.5 3.5 Riser1Pos Riser2Pos 4.0 5.5 0.2 0.6 3400 4200 9.0 11.0 0.3 0.6 3.5 5.0 4.0 5.5 BatchTime 1 Problem 2 (a) The output is below. The variables GateDiam and RiserDiam are sta- tistically significant at level 0.05. GateDiam has a negative slope so an increase in GateDiam decreases BatchTime . RiserDiam has a positive slope so an in- crease in RiserDiam increases BatchTime . We can see in the ANOVA table that GateDiam has a much larger Sum Sq than RiserDiam , so compared to the other variables, GateDiam has a much larger effect on BatchTime . (b) The estimated variance of the errors is 16,988. > summary(cast_lm) Call: lm(formula = BatchTime ˜ ., data = cast) Residuals: Min 1Q Median 3Q Max-226.4 -71.8 -11.9 60.6 389.9 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3739.6 394.4 9.48 3.4e-15 *** GateDiam-1042.9 96.5 -10.81 < 2e-16 *** CupHeight-34.2 34.3 -1.00 0.322 SprueHeight 20.5 24.2 0.84 0.400 RiserDiam 58.9 25.5 2.31 0.023 * SprueDiamBot 130.5 110.5 1.18 0.241 SprueDiamTop 132.6 79.6 1.67 0.099 ....
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This note was uploaded on 11/01/2011 for the course ORIE 3120 taught by Professor Jackson during the Spring '09 term at Cornell.

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multipleRegressionLabSolutions - Homework#8 Multiple Linear...

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