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lecture6solutions

lecture6solutions - Problem 6.8 Pag.249 1 x h =(1 5 4 ˆ Y...

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ISYE 6414 - Spring 2009 Solution lecture 5 The Linear Model: Multiple Regression Problem 6.1 Pag.248 In solution lecture 5. .. Problem 6.2 Pag.248 In solution lecture 5. .. Problem 6.3 Pag.248 In solution lecture 5. .. Problem 6.4 Pag.248 In solution lecture 5. .. Problem 6.6 Pag.248 1. H 0 : β 1 = β 2 = 0 vs. H a : { β 1 6 = 0 } ∪ { β 2 6 = 0 } . MSR = 936 . 35, MSE = 7 . 254. F * = MSR MSE = 129 . 083. F (0 . 99 , 2 , 13) = 6 . 70. And given that F * > 6 . 7, we reject the null hypothesis and accept that there is a regression relation. 2. P - value = P ( F (2 , 13) > 129 . 083 ) 0. 3. s ( b 1 ) = 0 . 301 , s ( b 0 ) = 0 . 673. B = t (0 . 9975 , 13) = 3 . 372. 3 . 41 β 1 5 . 44 2 . 106 β 2 6 . 644 4. Ellipsoidal joint confidence area: Using in R: g=lm(y~x1+x2,data=data) v=vcov(g) v=v[2:3,2:3] plot(ellipse(v,centre=c,level=0.99),type="l") The joint confidence area is plotted in figure 1.
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Unformatted text preview: Problem 6.8 Pag.249 1. x h = (1 , 5 , 4). ˆ Y h = x T h · b = 77 . 275. V ar ± ˆ Y h ² = MSE · x T h ( X T X )-1 x h = 1 . 127 2 Then the 99% confidence interval is: 77 . 275 ± 3 . 012 · 1 . 127 ⇒ 73 . 88 ≤ E ( Y h ) ≤ 80 . 670 2. V ar ± ˆ Y new ² = MSE · h 1 + x T h ( X T X )-1 x h i = 2 . 919 2 Then the 99% prediction interval is: 77 . 275 ± 3 . 012 · 2 . 919 ⇒ 68 . 483 ≤ ( Y new ) ≤ 86 . 067 1 Figure 1: Joint confidence area (99%). Problem 6.22 Pag.253 In solution lecture 5. .. Problem 6.23 Pag.253 In solution lecture 5. .. 2...
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lecture6solutions - Problem 6.8 Pag.249 1 x h =(1 5 4 ˆ Y...

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