hw3_BowenXiao.pdf - hw3_BowenXiao Bowen Xiao Problem 1 1.1...

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hw3_BowenXiaoBowen XiaoJanuary 25, 2018Problem 11.1As we can see in the following scatterplot matrix, marginal plot of Y versus X2 shows their positive linearrelationship ignoring X1. Marginal plot of Y versus X1 shows their positive linear relationship ignoring X2.Besides, X1 and X2 are positive linearly correlated.So marginal scatterplots for Y versus X1 and X2 are NOT going to be informative for the strength of linearrelationship between the predictor and each of the covariates in the multiple regression, since their roles inpredicting the response will be overlapping.library(alr4)X1<-Rateprof$easinessX2<-Rateprof$raterInterestY<-Rateprof$qualitypairs(~Y+X1+X2,main="Scatterplot Matrix")Y1.52.53.54.51.53.04.51.53.04.5X11.52.53.54.51234512345X2Scatterplot Matrix1
1.2From the following table, we can see that estimated residual variance, also called residual mean square isˆσ2=RSSn-3= 0.387, which is an unbiased estimator of variance of, orσ2. It measures deviations from anexact linear relationship between predictor and covariates, which may include measurement error, unobservedvariabes, inherent randomness, etc.The coefficient of determination isR2= 1-RSSSY Y=Corr(Y,ˆY)2= 0.45, which is also the square of thesample correlation between observed and fitted values. It provides a measure of how well observed outcomesare replicated by the model, more specifictly, 45% of total variation of outcomes can be explained by themodel.

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