Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig
9.4. Multiple Comparisons 525 There are R commands that compute the cdf of noncentralχ^2 andFrandom variables. For example, supp ...
526 Inferences About Normal Linear Models of the hypotheses of equal means, (9.2.2). In practice, besides this test, statisticia ...
9.4. Multiple Comparisons 527 Bonferroni confidence interval forμj−μj′is X·j−X·j′±tα/(2k),n−bσˆΩ √ 1 nj + 1 nj′ (9.4.3) While th ...
528 Inferences About Normal Linear Models For the unbalanced case, this suggests the following intervals X·j−X·j′± q 1 −α,b,n−b ...
9.4. Multiple Comparisons 529 > fit <- lm(speed~factor(car)) > anova(fit) ### F-Stat and p-value 25.145 1.903e-08 > ...
530 Inferences About Normal Linear Models Acura Ferrair Lotus Porsche Viper 160 165 170 175 180 Speed Figure 9.4.1:Boxplot of ca ...
9.5. Two-Way ANOVA 531 9.4.6.Extend the Bonferroni procedure to simultaneous testing. That is, suppose we havemhypotheses of int ...
532 Inferences About Normal Linear Models and H 0 B: β 1 =···=βb=0versusH 1 B:βj =0,forsomej. (9.5.4) IfH 0 Ais true, then by (9 ...
9.5. Two-Way ANOVA 533 Since these are sums of squares, the minimizing values, (mles), must be ˆμ=X··,ˆαi=Xi·−X··,andβˆj=X·j−X·· ...
534 Inferences About Normal Linear Models independent with the commonN( √ aμ, σ^2 ) distribution; see Exercise 9.5.2. Hence, by ...
9.5. Two-Way ANOVA 535 Under the additive model, (9.5.1), the mean of each cell depended on its row and column, but often the me ...
536 Inferences About Normal Linear Models LetQ′′ 3 denote the numerator of ˆσ^2. The major hypotheses of interest for the intera ...
9.5. Two-Way ANOVA 537 Coarse Aggregate Content Binder-Grade 38% 41% 44% PG58 0.835 0.822 0.785 0.845 0.826 0.795 PG64 0.855 0.8 ...
538 Inferences About Normal Linear Models 0.78 0.80 0.82 0.84 0.86 Binder mean of Conductivity PG58 PG64 PG70 Aggregrate (^3841) ...
9.6. A Regression Problem 539 9.5.8.Given the following observations in a two-way classification witha=3, b=4,andc= 2, compute t ...
540 Inferences About Normal Linear Models grade in calculus. Frequently, one of these variables, sayx, is known in advance of th ...
9.6. A Regression Problem 541 y x xi yi y^i Figure 9.6.1:The plot shows the least squares fitted line (solid line) to a set of d ...
542 Inferences About Normal Linear Models Setting∂H(α, β)/∂α=0,weobtain ∑n i=1 yi−nα−β ∑n i=1 (xi−x)=0. (9.6.2) Since ∑n i=1(xi− ...
9.6. A Regression Problem 543 Since ˆαis a linear function of independent and normally distributed random variables, ˆαhas a nor ...
544 Inferences About Normal Linear Models In this equation,Qrepresents the sum of the squares ofnindependent random variables th ...
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