hw12_solutions_to_post - Andrea Gruber Jery Stedinger Fall...

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Andrea Gruber & Jery Stedinger Fall 2007 HW #12 Selected Solutions # 18abcd Section 12.2, Devore 7 p 466, (Devore 6 p 518) x = temperature (F), y = deflection adjustment factor (y>=0) n =15, 1425 i x = , 10.68 i y = , 2 139037.25 i x = , 2 7.8518 i y = , 987.645 i i x y = a) Compute 1 ˆ β , 0 ˆ β , and the equation of the estimated regression line. Graph the estimated line. ( 29 ( 29 ( 29 = = - - - = n i i n i i i x x y y x x 1 2 1 1 ˆ β ^ 1 1 1 1 2 2 2 1 1 1 987.645 1425(10.68) /15 0.00736 139037.25 (1425 ) /15 1 n n n i i i i i i i n n i i i i x y x y n x x n β = = = = = - - = = = - - - � � x y 1 0 ˆ β β - = ( 29 ^ 0 1 1 1 1 1 ˆ 10.68 ( 0.00736)(1425) 1.4112 15 n n i i i i y x n β β = = = - = - - = So, 411 . 1 0 = β , 00736 . 0 ˆ 1 - = β Regression function: y = 1.411 – 0.00736 x b) What is the estimate of expected change in the deflection adjustment factor when temperature is increased by 1 degree F? Expected change in y when x is increased by 1 o F = 1 ˆ β = -0.00736 c) Suppose temperature were measured in C rather than in F. What would be the estimated regression line? Answer part (b) for an increase of 1C. [Hint: F= (9/5)C +32; now substitute for the “old x” in terms of the “new x”.] With x now denoting temperature in C , + + = 32 5 9 ˆ ˆ 1 0 x y β β ( 29 x x 0132484 . 175695 . 1 ˆ 5 9 ˆ 32 ˆ 1 1 0 - = + + = β β β , so the new 1 ˆ β is -.0132484 and the new 175695 . 1 ˆ 0 = β . Expected change in y when x is increased by 1 o C = 1 ˆ β = -0.01325 d) If a 200 F surface temperature were within the realm of possibility, would you use the estimated line of part (a) to predict deflection factor for this temperature?
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