ass4 - STAT3503 Assignment # 4 Due Aug. 6 IN Tutorial....

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STAT3503 Assignment # 4 Due Aug. 6 IN Tutorial. Question 1. ( Use SAS to solve this question ) In a small-scale experimental study of the relation between degree of brand liking (Y) and moisture content ( X 1 ) and sweetness ( X 2 ) of the product, the following results were obtained from the experiment based on a completely randomized design. (data in WebCT \ SAS code). (a) [1 points] Test whether there is a regression relation, using α = 0 . 01. (b) [1 points] What is the P-value of the test in part (a)? (c) [1 points] Estimate β 1 and β 2 jointly by the Bonferroni procedure, using a 99 percent family confidence coefficient. (d) [1 points] Calculate the coefficient of multiple determination R 2 . (e) [1 points] Calculate the coefficient of simple determination R 2 between Y i and b Y i . Does it equal the coefficient of multiple determination in part (d)? (f) [1 points] Obtain the extra sums of squares associated with X 1 and with X 2 , given X 1 . (g) [1 points] Test whether X 2 can be dropped from the regression model given that X 1 retained. Use F * test statistic and level of significance 0.01. What is the P-value of the test? (h) [1 points] Calculate R 2 Y 1 ,R 2 Y 2 ,R 2 12 ,R 2 Y 1 | 2 ,R 2 Y 2 | 1 . (i) [1 points] Fit regression model( Y i = β 0 + β 1 X i 1 + β 2 X i 2 + ε i ) to the data. (j) [1 points] Fit first-order simple linear regression model( Y i = β 0 + β 1 X 1 + ε i ) for relating brand liking( Y ) to moisture content( X 1 ). (k) [1 points] Compare the estimated regression coefficient for moisture content obtained in part (j) with the corresponding coefficient obtained in part (i). (l) [1 points] Does SSR( X 1 ) equal SSR( X 1 | X 2 ) (m) [1 points] Regress Y on X 2 using simple linear regression model and obtain the residuals. (n) [1 points] Regress X 1 on X 2 using simple linear regression model and obtain the residuals. 1
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(o) [1 points] Calculate the coefficient of simple correlation between the two sets of residuals in (m) and (n) and show that it equals r Y 1 | 2 SOLUTION (a) H 0 : β 1 = β 2 = 0 , H a : Not all β i = 0 , i = 1 , 2 F * = MSR MSE = 936 . 35 7 . 25385 = 129 . 08 > F (0 . 99; 2 , 13) = 6 . 7 So, conclude H a . (b) P-value 0 (c) 4 . 42500 ± 3 . 372467941 × 0 . 30112 , 3 . 40948 β 1 5 . 44052 4 . 37500 ± 3 . 372467941 × 0 . 67332 , 2 . 10424 β 2 6 . 64576 (d) R 2 = 0 . 9521. (e)
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ass4 - STAT3503 Assignment # 4 Due Aug. 6 IN Tutorial....

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