Homework 11- stats

# Homework 11- stats - Multiple R-squared: 0.7175, Adjusted...

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Homework 11 Exercises with R 20. > x<-c(.05,.10,.11,.12,.31,.37,.42,.58,.68,.68,.73,.85,.92) > y<-c(.48,.55,.48,.50,.58,.52,1.02,.86,.86,1.00,.88,1.04,1.70) > z<-lm(y~x) > summary(z) Call: lm(formula = y ~ x) Residuals: Min 1Q Median 3Q Max -0.20283 -0.14691 -0.02255 0.06655 0.44541 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.36510 0.09904 3.686 0.003586 ** x 0.96683 0.18292 5.286 0.000258 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.1932 on 11 degrees of freedom
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Unformatted text preview: Multiple R-squared: 0.7175, Adjusted R-squared: 0.6918 F-statistic: 27.94 on 1 and 11 DF, p-value: 0.0002581 a) From this data we get the following: 1 β (hat)= 0.96683 β o(hat)= 0.36510 y(hat)= 0.36510 + 0.96683x b) when x=.5 y(hat)= 0.36510 + 0.96683(.5)= .8454 c) Estimate of σ? σ= √SSE/n-2= 0.1932 d) Total Variation: SST= 1.4533 (this from by-hand calculation) r^2= 1 - .4106/1.4533= .7175 Or 71.75% of the total variation can be explained by the model....
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## This note was uploaded on 04/29/2008 for the course STAT 1211 taught by Professor Hernandez during the Spring '08 term at Columbia.

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