E 9 variability explained by the regression on x is

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Unformatted text preview: SYY − RSS = SSreg = 8 SXY 2 SXX Multiple Correlation Coecient R 2 The multiple correlation coecient or coecient of determination R2 = = SSreg SYY − RSS SXY 2 RSS /(n − 1) = = =1− SYY SYY SXX · SYY SYY /(n − 1) proportion of Note that x 's and R2 y 's, i.e., 9 variability explained by the regression on X. is just the square of the Pearson correlation between i.e., The adjusted Y √ r = SXY / SXX · SYY . ¯ R2 = R2 uses n−2 in the RSS denominator above, RSS /(n − 2) n−1 ¯ R2 = 1 − =1− (1 − R 2 ) SYY /(n − 1) n−2 Comments with(spirit,plot(gas,weight)) # avoids the clumsy plot(spirit$gas,spirit$weight, xlab="gas",ylab="weight") # similarly, use fit <- with(spirit,lm(weight~gas)) # but not with(spirit,fit <- lm(weight~gas)) # Hall’s report gives gasoline at # 6.12 lbs per gallon # It would seem that they figured # the weight of aircraft from that 10 Aircraft Weight vs Takeo Distance with(spirit, plot(TO.distance,weight, xlim=c(200,3000),ylim=c(2000,6000))) x <- seq(200,3000,10) y <- 10^2.6503023 * x^0.3237002; lines(x,y) points(c(2000,3000),c(5000,5500),pch=16,col="red") with(spirit, plot(TO.distance,weight,log="xy", xlim=c(200,3000),ylim=c(2000,6000))) fit <- with(spirit, lm(log10(weight)~log10(TO.distance))) fit$coef (Intercept) log10(TO.distance) 2.6503023 0.3237002 abline(fit,col="blue") points(c(2000,3000),c(5000,5500),pch=16,col="red") qqnorm(fit$residuals); qqline(fit$residuals...
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