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solnsamplemidterm108

# solnsamplemidterm108 - Solution to the SAMPLE MIDTERM...

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Solution to the SAMPLE MIDTERM Statistics 108 1. a) ANOVA table Source df SS MS Regression 1 859.1 859.1 Error n-2=10 573.9 57.39 Total n-1=11 1433.0 b) Test H 0 : β 1 = 0 against H 1 : β 1 = 0 at level α = 0 . 05 F * = MSR/MSE = 859 . 1 / 57 . 39 = 14 . 970 . df=(1 , 10). F ( . 95; 1 , 10) = 4 . 96 . Since F * > F ( . 95; 1 , 10) we reject H 0 . p-value=area to the right of 14 . 970 under the F curve with df=(1,10). From the F-table, F ( . 995; 1 , 10) = 12 . 8 and F ( . 999; 1 , 10) = 21 . 0 . So the p-value is between .001 and .005. c) R 2 = SSR/SSTO = . 5995 About 60% of the variability in Physics score ( Y ) can be explained by its regression on Mathematics score ( X ). 2. a) b 1 = ( X i - ¯ X )( Y i - ¯ Y ) / ( X i - ¯ X ) 2 = 876 / 97 = 9 . 03093 b 0 = ¯ Y - b 1 ¯ X = 160 - (9 . 03093)(4 . 6) = 118 . 45772 Fitted regression line ˆ Y = 118 . 4577 + 9 . 0309 X Estimated cancer mortality at X = 3 . 7 is ˆ Y = 118 . 4577 + (9 . 0309)(3 . 7) = 151 . 8720 . b) SSE = ( Y i - ¯ Y ) 2 - b 2 1 ( X i - ¯ X ) 2 = 9400 - (9 . 03093) 2 (97 . 0) = 1488 . 90342 . MSE = SSE/ ( n - 2) = 1488 . 90342 / 7 = 212 . 70049 s 2 ( b 1 ) = MSE/ ( X i - ¯ X ) 2 = 212 . 70049 / 97 = 2 . 19279 , s ( b 1 ) = 1 . 48081 . 95% confidence interval for β 1 is b 1 ± t ( . 975; 7) s ( b 1 ), i.e., 9 . 03093 ± (2 . 365)(1 . 48081), i.e., 9 . 031 ± 3 . 502, i.e., (5 . 529 , 12 . 533) c) At X h = 3 . 7, ˆ Y h = 151 . 8720 (from part (a)).

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solnsamplemidterm108 - Solution to the SAMPLE MIDTERM...

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