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# hw3_soln4 - xy = ∑ i i y x ∑ i x ∑ i y/n =...

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HW Set 3: Due 4/20 in quiz session. HW8: hw_O (lecture 9), 3.18(a,b), 3.47(a,b). Graded problems (and points): TBA. 18. (a) To obtain the least squares regression equation, first we will compute the slope and the vertical intercept using the equations provided in Section 3.3. ( 29 ( 29 ( 29 ( 29 62615 . 14 517 652289939 . 14 346 : Also 652289939 . 93 . 002 , 20 71 . 047 , 13 , 93 . 002 , 20 14 517 095 , 39 71 . 047 , 13 14 346 517 825 , 25 2 = - = - = = = = = - = = - = x b y a S S b So S S xx xy xx xy Thus, the equation for the least squares line is: x y 6523 . 0 626 . 0 ˆ + = (b) ( 29 46 . 23 35 65228939 . 62615 . ˆ , 35 When = + = = y x The corresponding residual is: ( 29 ( 29 46 . 2 46 . 23 21 ˆ - = - = - = y y residual 47 (a) Since stride rate is being predicted, y = stride rate and x = speed. Therefore, SS xx = 2 i x -( i x ) 2 /n = 3880.08 - (205.4) 2 /11 = 44.7018, SS yy = 2 i y - ( i y ) 2 /n = 112.681 - (35.16) 2 /11 = .2969, and SS
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Unformatted text preview: xy = ∑ i i y x- ( ∑ i x )( ∑ i y )/n = 660.130 - (205.4)(35.16)/11 = 3.5969. Therefore, b = SS xy /SS xx = 3.5969/44.7018 = .0805 and a = (35.16/11) - (.0805) (205.4/11) = 1.6932. The least squares line is then y ˆ = 1.6932 + .0805x. (b) Predicting speed from stride rate means that y = speed and x = stride rate. Therefore,interchanging the x and y subscripts in the sums of squares computed in part (a), we now have SS xx = .2969 and SS xy = 3.5969 (note that SS xy does not change when the roles of x and y are reversed). The new regression line has a slope of b = SS xy /SS xx = 3.5969/.2969 = 12.1149 and an intercept of a = (205.4/11) - (12.1149)( 35.16/11) = -20.0514; that is, y ˆ = -20.0514 + 12.1149x....
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