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# FRADE_hw5 - STA5166 HW5 Problem chapter 9.2#=parta#each...

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STA5166 HW5 Jaime Frade Problem chapter 9.2 #=================parta ##each pair of observations occurs in the same block one time, lambda=1 #=================partb ##Efficiency factor ##E = [(lambda)(t)]/[rk] lambda=1 ##how many times each pair is repeated t = 7 ##number of treatments, total of columns r = 4 ##number of item w/in columns k = 4 ##number of items w/in each row E = ((lambda)*(t))/(r*k) E = 2*7/4*4 =14/16 #=================partC #y_ij = \mu _ \beta_j + \tau_i + \epsilon_ij i=1, 2, 3 , 4, 5, 6, 7 (number of colms) j = 1-7 (number of rows) # #\beta_j = jth block as block effect #\tau_i = ith treatment #\mu is general mean #\epsilon = experimental error, mean=0 variance \sigma^2 normal iid # #==========part c fit1= aov(Data~factor(Run)+factor(Voltage), data=BIBProb2) fit1 Call: aov(formula = Data ~ factor(Run) + factor(Voltage), data = BIBProb2) Terms: factor(Run) factor(Voltage) Residuals Sum of Squares 47866.28 275795.04 9315.78 Deg. of Freedom 6 7 14 Residual standard error: 25.79559 Estimated effects may be unbalanced

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STA5166 HW5 Jaime Frade #==========part d #==========part e > lndata = log(BIBProb2$Data) > lndata [1] 3.6425737 1.6937791 0.6729445 -0.5978370 5.3946270 2.0360120 [7] 0.9321641 -0.4004776 5.6015652 5.3016618 1.8309802 -0.2744368 [13] 5.8864928 5.1388526 3.8161727 1.1693814 5.3941729 4.0384794 [19] 2.2321626 -0.4942963 5.7059801 4.0134960 2.3427669 1.9726912 [25] 5.2511209 2.1679102 1.9344158 0.7929925 > > BIBProb2_2= data.frame(lndata, data=BIBProb2) > BIBProb2_2 lndata data.Data data.Run data.Voltage 1 3.6425737 38.19 1 32 2 1.6937791 5.44 1 40 3 0.6729445 1.96 1 44 4 -0.5978370 0.55 1 58 5 5.3946270 220.22 2 24 6 2.0360120 7.66 2 36 7 0.9321641 2.54 2 44 8 -0.4004776 0.67 2 48 9 5.6015652 270.85 3 24 STA5166 HW5 Jaime Frade 10 5.3016618 200.67 3 28 11 1.8309802 6.24 3 40 12 -0.2744368 0.76 3 48 13 5.8864928 360.14 4 24 14 5.1388526 170.52 4 28 15 3.8161727 45.43 4 32 16 1.1693814 3.22 4 44 17 5.3941729 220.12 5 28 18 4.0384794 56.74 5 32 19 2.2321626 9.32 5 36 20 -0.4942963 0.61 5 48 21 5.7059801 300.66 6 24 22 4.0134960 55.34 6 32 23 2.3427669 10.41 6 36 24 1.9726912 7.19 6 40 25 5.2511209 190.78 7 28 26 2.1679102 8.74 7 36 27 1.9344158 6.92 7 40 28 0.7929925 2.21 7 44 > fit2= aov(lndata~factor(data.Voltage)+ factor(data.Run), data=BIBProb2_2) > fit2 Call: aov(formula = lndata ~ factor(data.Voltage) + factor(data.Run), data = BIBProb2_2) Terms: factor(data.Voltage) factor(data.Run) Residuals Sum of Squares 123.09915 0.28622 0.23430 Deg. of Freedom 7 6 14 Residual standard error: 0.1293674 Estimated effects may be unbalanced > summary(fit2) Df Sum Sq Mean Sq F value Pr(>F) factor(data.Voltage) 7 123.099 17.586 1050.7691 < 2e-16 *** factor(data.Run) 6 0.286 0.048 2.8504 0.04985 * Residuals 14 0.234 0.017 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 > par(mfrow=c(1,1)) > plot(fit2$fitted, fit2\$resid)

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STA5166 HW5 Jaime Frade > fit_BIBprob2 = aov(Data~factor(Run)+factor(Voltage), data=BIBProb2 ) > fit_BIBprob2
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FRADE_hw5 - STA5166 HW5 Problem chapter 9.2#=parta#each...

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