# ass3 - STAT3503 Assignment # 3 Due July. 23 IN Tutorial....

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Unformatted text preview: STAT3503 Assignment # 3 Due July. 23 IN Tutorial. Question 1. ( Use SAS to solve this question ) Sixteen batches of plastic were made, and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below; X is the elapsed time in hours, and Y is hardness in Brinell units. Assume that first-order regression is appropriate. . Assume that first-order regression model( Y = β + β 1 X + ε ) is appropriate (a) [7 points] Using matrix methods, obtain the following: (1) Design matrix X , (2) ( X X )- 1 , (3) b β , (4) b Y , (5) H , (6) SSE, (7) s 2 ( β ), (8) SSR, (9) SSTO, (10) R 2 (11) s 2 ( pred ) when X h = 30. SOLUTION (1) X = 1 16 1 16 1 16 1 16 1 24 1 24 1 24 1 24 1 32 1 32 1 32 1 32 1 40 1 40 1 40 1 40 (2) ( X X )- 1 = . 675- . 021875- . 021875 . 0007813 1 (3) b β = 168 . 6 2 . 034375 (4) b Y = X b β = HY = 201 . 15 201 . 15 201 . 15 201 . 15 217 . 425 217 . 425 217 . 425 217 . 425 233 . 7 233 . 7 233 . 7 233 . 7 249 . 975 249 . 975 249 . 975 249 . 975 (5) H = . 175 . 175 . 175 . 175 . 1 . 1 . 1 . 1 . 025 . 025 . 025 . 025- . 05- . 05- . 05- . 05 . 175 . 175 . 175 . 175 . 1 . 1 . 1 . 1 . 025 . 025 . 025 . 025- . 05- . 05- . 05- . 05 . 175 . 175 . 175 . 175 . 1 . 1 . 1 . 1 . 025 . 025 . 025 . 025- . 05- . 05- . 05- . 05 . 175 . 175 . 175 . 175 . 1 . 1 . 1 . 1 . 025 . 025 . 025 . 025- . 05- . 05- . 05- . 05 . 1 . 1 . 1 . 1 . 075 . 075 . 075 . 075 . 05 . 05 . 05 . 05 . 025 . 025 . 025 . 025 . 1 . 1 . 1 . 1 . 075 . 075 . 075 . 075 . 05 . 05 . 05 . 05 . 025 . 025 . 025 . 025 . 1 . 1 . 1 . 1 . 075 . 075 . 075 . 075 . 05 . 05 . 05 . 05 . 025 . 025 . 025 . 025 . 1 . 1 . 1 . 1 . 075 . 075 . 075 . 075 . 05 . 05 . 05 . 05 . 025 . 025 . 025 . 025 . 025 . 025 . 025 . 025 . 05 . 05 . 05 . 05 . 075 . 075 . 075 . 075 . 1 . 1 . 1 . 1 . 025 . 025 . 025 . 025 . 05 . 05 . 05 . 05 . 075 . 075 . 075 . 075 . 1 . 1 . 1 . 1 . 025 . 025 . 025 . 025 . 05 . 05 . 05 . 05 . 075 . 075 . 075 . 075 . 1 . 1 . 1 . 1 .....
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## This note was uploaded on 09/30/2010 for the course STAT 3503 taught by Professor Smills during the Spring '07 term at Carleton CA.

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ass3 - STAT3503 Assignment # 3 Due July. 23 IN Tutorial....

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