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hw4sol - STAT 4220 HW4 Solution 1 Problem 1(a See the...

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STAT 4220 HW4 Solution 1 Problem 1 (a) See the appendix for R code. Fitting the model yields the following output: > summary(g) Call: lm(formula = y ˜ factor(x)) Residuals: Min 1Q Median 3Q Max -2.64889 -0.44889 -0.04889 0.55111 2.15111 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 22.2989 0.1355 164.515 < 2e-16 *** factor(x)2 0.7911 0.2711 2.918 0.00424 ** factor(x)3 0.8225 0.2783 2.956 0.00379 ** factor(x)4 0.2761 0.2647 1.043 0.29903 factor(x)5 0.6044 0.2711 2.230 0.02773 * factor(x)6 -1.1689 0.2711 -4.312 3.46e-05 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: 0.9093 on 114 degrees of freedom Multiple R-squared: 0.313, Adjusted R-squared: 0.2829 F-statistic: 10.39 on 5 and 114 DF, p-value: 3.152e-08 > summary.aov(g) Df Sum Sq Mean Sq F value Pr(>F) factor(x) 5 42.940 8.5879 10.388 3.152e-08 *** Residuals 114 94.248 0.8267 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 From the ANOVA table, we see that with p ¿ . 0001, the type of bird is very significant in determining the length of the cuckoo eggs. (b) The residual plot is generated with the following code: > plot(x,g$res,xlab="Cuckoo",ylab="Residuals",pch=20,col=3, main="Plot of residual versus factor levels",xaxt="n") > mtext(paste("MDWP"),side=1,at=1) > mtext(paste("TRP"),side=1,at=2) > mtext(paste("HGSPRW"),side=1,at=3) > mtext(paste("RBN"),side=1,at=4) > mtext(paste("PWGTL"),side=1,at=5) > mtext(paste("WREN"),side=1,at=6) 1
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-2 -1 0 1 2 Plot of residual versus factor levels Cuckoo Residuals MDWP TRP HGSPRW RBN PWGTL WREN (c) For the most part, the spread of the residuals seems to be fairly even across factor levels. We may have slightly smaller variance at the RBN and WREN factor levels, but it is negligible for our purposes. Deciding whether the assumption of constant variance holds based on these plots is always subjective. (d) The boxplot is generated with the following: plot(x,g$res,xlab="Cuckoo",ylab="Residuals",pch=20,col=3, main="Plot of residual versus factor levels",xaxt="n") mtext(paste("MDWP"),side=1,at=1) mtext(paste("TRP"),side=1,at=2) mtext(paste("HGSPRW"),side=1,at=3) mtext(paste("RBN"),side=1,at=4)
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