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HW Solutions Stat 77

# HW Solutions Stat 77 - A B Freq 11 4 12 4 13 4 21 4 22 4 23...

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A B Freq. X 1 X 2 X 3 X 4 X 1 X 3 X 1 X 4 X 2 X 3 X 2 X 4 1 1 4 1 1 0 1 0 1 0 0 0 1 2 4 1 1 0 0 1 0 1 0 0 1 3 4 1 1 0 1 1 1 1 0 0 2 1 4 1 0 1 1 0 0 0 1 0 2 2 4 1 0 1 0 1 0 0 0 1 2 3 4 1 0 1 1 1 0 0 1 1 3 1 4 1 1 1 1 0 1 0 1 0 3 2 4 1 1 1 0 1 0 1 0 1 3 3 4 1 1 1 1 1 1 1 1 1 c. X β entries: A B 1 1 µ .. + α 1 + β 1 + ( αβ ) 11 1 2 µ .. + α 1 + β 2 + ( αβ ) 12 1 3 µ .. + α 1 β 1 β 2 ( αβ ) 11 ( αβ ) 12 = µ .. + α 1 + β 3 + ( αβ ) 13 2 1 µ .. + α 2 + β 1 + ( αβ ) 21 2 2 µ .. + α 2 + β 2 + ( αβ ) 22 2 3 µ .. + α 2 β 1 β 2 ( αβ ) 21 ( αβ ) 22 = µ .. + α 2 + β 3 + ( αβ ) 23 3 1 µ .. α 1 α 2 + β 1 ( αβ ) 11 ( αβ ) 21 = µ .. + α 3 + β 1 + ( αβ ) 31 3 2 µ .. α 1 α 2 + β 2 ( αβ ) 12 ( αβ ) 22 = µ .. + α 3 + β 2 + ( αβ ) 32 3 3 µ .. α 1 α 2 β 1 β 2 + ( αβ ) 11 + ( αβ ) 12 + ( αβ ) 21 + ( αβ ) 22 = µ .. + α 3 + β 3 + ( αβ ) 33 d. ˆ Y = 7 . 18333 3 . 30000 X 1 + . 65000 X 2 2 . 55000 X 3 + . 75000 X 4 +1 . 14167 X 1 X 3 . 03333 X 1 X 4 + . 16667 X 2 X 3 + . 34167 X 2 X 4 α 1 = µ 1 . µ .. e. Source SS df Regression 373 . 125 8 X 1 212 . 415 1] A X 2 | X 1 7 . 605 1] A X 3 | X 1 , X 2 113 . 535 1] B X 4 | X 1 , X 2 , X 3 10 . 125 1] B X 1 X 3 | X 1 , X 2 , X 3 , X 4 26 . 7806 1] AB X 1 X 4 | X 1 , X 2 , X 3 , X 4 , X 1 X 3 . 2269 1] AB X 2 X 3 | X 1 , X 2 , X 3 , X 4 , X 1 X 3 , X 1 X 4 1 . 3669
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