HW3soln

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Unformatted text preview: q u a r e d : 0 . 9 9 4 5 F− s t a t i s t i c : 7 2 9 . 2 on 1 and 3 DF, p−v a l u e : 0 . 0 0 0 1 1 1 4 f. From the summary above, t test has t value -27 and p value 0.000111 (or F test has p value 0.0001114). So there is a significant relationship between AverageWeight and Age. 3. Solution a. Here is the summary: > f i t 1=lm ( c o l o n i e s ˜ dose , data=s a l m o n e l l a ) > summary ( f i t 1 ) Call : lm ( f o r m u l a = c o l o n i e s ˜ dose , data = s a l m o n e l l a ) Residuals : Min 1Q − 13.488 − 8.991 Median − 1.569 3Q 7.569 Max 31.736 Coefficients : Estima te Std . E r r o r t ( Intercept ) 27.683154 3.462169 dose 0.005805 0.008006 −−− S i g n i f . c o d e s : 0 ∗∗∗ 0 . 0 0 1 ∗∗ v a l u e Pr ( > | t | ) 7 . 9 9 6 5 . 5 8 e −07 ∗∗∗ 0.725 0.479 0.01 ∗ 0.05 . 0.1 1 R e s i d u a l s t a n d a r d e r r o r : 1 2 . 0 8 on 16 d e g r e e s o f freedom M u l t i p l e R−s q u a r e d : 0 . 0 3 1 8 1 , Adjusted R−s q u a r e d : − 0.0287 F− s t a t i s t i c : 0 . 5 2 5 7 on 1 and 16 DF, p−v a l u e : 0 . 4 7 8 9 b. Lacking of Fitness testing is possible because the data contain replicates (multiple y values for the same x value). You can see it by listing the data. > salmonella [ 1 : 5 , ] c o l o n i e s dose 1 15 0 2 21 0 3 29 0 4 16 10 5 18 10 4 c. Here is the R output: > f i t 2=lm ( c o l o n i e s ˜ f a c t o r ( d o s e ) , data=s a l m o n e l l a ) > anova ( f i t 1 , f i t 2 ) A n a l y s i s o f V a r i a n c e Table Model 1 : c o l o n i e s ˜ d o s e Model 2 : c o l o n i e s ˜ f a c t o r ( d o s e ) Res . Df RSS Df Sum o f Sq F Pr(>F) 1 16 2 3 3 5 . 1 2 12 1 0 9 1 . 3 4 1243.7 3.4189 0.04373 ∗ −−− S i g n i f . c o d e s : 0 ∗∗∗ 0 . 0 0 1 ∗∗ 0 . 0 1 ∗ 0 . 0 5 . 0.1 1 d. Notice F-statistic is 3.4189 and the p-value is 0.04373. So there is a lack of fit. e. Here is the R code and output. The estimate of pure error variance is 90.94. > d o s e s=unique ( s...
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This homework help was uploaded on 03/28/2014 for the course STAT 425 at University of Illinois, Urbana Champaign.

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