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# homework03Solutions - Stat 401G Homework 3 SOLUTIONS 1 A...

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Stat 401G Homework 3 SOLUTIONS 1. A study to assess the capability of subsurface flow wetland systems to remove biochemical oxygen demand (BOD) and various other chemical constituents resulted in the accompanying data on x=BOD mass loading (kg/ha/d) and y=BOD mass removal (kg/ha/d) (“Subsurface Flow Wetland- A Performance Evaluation,” Water Envir. Res. , 1995: 244-247). x 3 8 10 11 13 16 27 30 35 37 38 44 103 142 y 4 7 8 8 10 11 16 26 21 9 31 30 75 90 In this problem, simple linear regression for predicting y from x will be performed. Hand calculations will be required throught and the following quantities will be helpful: s 2 x = 1538 . 687 ¯ x = 36 . 92857 ¯ y = 24 . 71429 14 X i =1 ( x i - ¯ x ) 2 = 20002 . 93 14 X i =1 ( x i - ¯ x ) ( y i - ¯ y ) = 13047 . 71 (a) Find ˆ β 0 and ˆ β 1 . ˆ β 1 = n i =1 ( x i - ¯ x )( y i - ¯ y ) n i =1 ( x i - ¯ x ) 2 = 13047 . 71 20002 . 93 = 0 . 65229 ˆ β 0 = ¯ y - ˆ β 1 ¯ x = 24 . 71429 - 0 . 65229 (36 . 92857) = 0 . 6261531 (b) Create a table of fitted values and residuals. In the table below, you only needed the 3 rd and 4 th columns. I included others that might be helpful. In particular, the last column for y i - ¯ y

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homework03Solutions - Stat 401G Homework 3 SOLUTIONS 1 A...

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