RegressionInClassSolutions

# RegressionInClassSolutions - ESI 6321 APPLIED PROBABILITY...

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ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 January 13, 2008 IN-CLASS ASSIGNMENT - SOLUTIONS Problem 1: (a) S XY = x i y i i ! " n x y = 1083.67 " 20 1478 20 # \$ % ( 12.75 20 # \$ % ( = 141.445 S XX = x i 2 i ! " n x 2 = 143,215.8 " 20 1478 20 # \$ % ( 2 = 33,991.6 ˆ ! 1 = S XY S XX = 141.445 33991.6 = 0.00416 ˆ 0 = y " ˆ 1 x = 12.75 20 " 0.00416 1478 20 # \$ % ( = 0.33 (b) ˆ y = ˆ 0 + ˆ 1 x = 0.33 + 0.00416 " 85 = 0.684 . (c) ˆ μ = ˆ 0 + ˆ 1 x = 0.33 + 0.00416 " 90 = 0.704 . (d) 1 ˆ 0.00416 = . (e) Denote the temperature in ° C by c , i.e., x = 9 5 c + 32 . This means that the new regression line becomes: ˆ y = ˆ 0 + ˆ 1 x = ˆ 0 + ˆ 1 9 5 c + 32 " # \$ % = ˆ 0 + 32 ˆ 1 ( ) + 9 5 ˆ 1 c = 0.46 + 0.00749 c . (f) 1 9 ˆ 0.00749 5 = .

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(g) The coefficient of determination is equal to R 2 = 1 ! SSE SST = 1 ! y i 2 i " ! ˆ
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## RegressionInClassSolutions - ESI 6321 APPLIED PROBABILITY...

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