Unformatted text preview: S xx and ˆ σ = SSE/ ( n2) . It can be shown that SSE = S yyS 2 xy /S xx , we get S ˆ β 1 = 1 √ n2 q S yy S xx( S xy S xx ) 2 . Then we reject H if  t  > t α/ 2 ,n2 at 100(1α )% signiﬁcance. We don’t usually compute the test statistic by hand. Use Rpackage. Example. We continue Lecture 19 example. >summary(lm(y˜x)) Call: lm(formula = y ˜ x) Residuals: Min 1Q Median 3Q Max10.908 6.312 1.758 4.354 10.836 Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 29.48 13.23 2.22 0.06 x 0.55 0.17 3.12 0.01 *Signif. codes: 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ Residual standard error: 7.647 on 8 degrees of freedom Multiple RSquared: 0.5519, Adjusted Rsquared:0.4959 Fstatistic:9.854o n 1 and 8 DF, pvalue: 0.01383...
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 Fall '04
 Chung
 Statistics, Linear Regression, Normal Distribution, Regression Analysis, maximum likelihood estimation, yj, cj yj, linear model Yj

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