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Assignment 3

# Assignment 3 - STAT 331/361/SYDE 334 Assignment 3 Due...

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STAT 331/361/SYDE 334 Assignment 3 Due: Thursday, March 13 th in class 1. Consider the general model y = X β + ε , where ε ~ N(0 , σ 2 I). We know that 1 ˆ ( ' ) ' X X X β = y and so ˆ H y μ = and ( e I H = ) y , where H = X ( X X ) –1 X .’ Prove that ˆ μ and e are independent. (Hint: see page 96 of the textbook for a similar proof.) 2. The table below displays annual sales data ( y , in 100,000s of dollars) from 15 sales districts. The promotional expenditures ( x 1 , in 1000s of dollars), number of active accounts ( x 2 ), number of competing brands ( x 3 ), and district potential ( x 4 , coded as a number between 1 and 20) for each district are also given. (Data is also available in the file sales.txt) y x 1 x 2 x 3 x 4 79.3 5.5 31 10 8 200.1 2.5 55 8 6 163.2 8.0 67 12 9 200.1 3.0 50 7 16 146.0 3.0 38 8 15 177.7 2.9 71 12 17 30.9 8.0 30 12 8 291.9 9.0 56 5 10 165.0 4.0 42 8 4 339.4 6.5 73 5 16 159.6 5.5 60 11 7 86.3 5.0 44 12 12 237.5 6.0 50 6 6 107.2 5.0 39 10 4 155.0 3.5 55 10 4 a. A model with all four regressors is proposed: y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + ε , where ε ~ N(0, σ 2 ). Interpret the parameters β 0 , β 1 , and β 3 .

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Assignment 3 - STAT 331/361/SYDE 334 Assignment 3 Due...

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