Assignment 4 suggested solution (Posted on 27 Mar)

Assignment 4 suggested solution (Posted on 27 Mar) - The...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT0302 Business Statistics Semester 2 2008/2009 Assignment 4 Suggested Solution 1. (i) Multiply the normalized equations by the coefficient of and add. a () ( ) ( ) 21 4 1 24 2 4 12 2 2 2 12 2 24 4 2 14 3 3 3 269 55 8 14 3 42 9 3 21 5 5 3 5 21 5 3 105 25 15 25 4 4 3 4 25 4 3 100 16 12 ab a b a b a b ×− =− − ×− =− − − = + ×= − × =− ⇒× = + × = + =+ + × = + = Multiply the normalized equations by the coefficient of b and add. ( ) ( ) ()( )() ()( ) 4 4 8 4 1 6 12 1 2 1 12 2 12 2 14 1 3 1 18 8 36 14 3 14 3 21 3 5 3 3 21 5 3 63 15 9 25 3 4 3 3 25 4 3 75 12 9 a b a b − = + ×− = − ×− = + = + × = + = + = + On solving the two equations 269 55 8 = + and 18 8 36 , this gives and 5.1294 a = 1.6399 b = − . (ii) The squared discrepancy is ( ) ( ) ( ) ( 222 2 2 4 2 2 12 3 14 5 3 21 4 3 25 Da b a b a b a b a b =−− − + − − + + − + + ) 2 The minimum squared discrepancy is ( ) 22 2 2 1 5.1294 4 1.6399 2 2 5.1294 1.6399 12 3 5.1294 1.6399 14 5 5.1294 3 1.6399 21 4 5.1294 3 1.6399 25 0.6639 D =−× −− +− +×− −× = 2. (i) ± 57.8043 1.4520 yx (ii) ± 57.8043 1.4520 74 165.25 y × = (iii) rank rank i dx y x 75 80 78 71 74 67 70 62 69 73 x rank 8 10 9 5 7 2 4 1 3 6 y 162 178 170 163 166 156 158 149 157 163 y rank 5 10 9 6.5 8 2 4 1 3 6.5 i d 3 0 0 -1.5 -1 0 0 0 0 -0.5 ( ) () 2 2222 3 0 0 1.5 1 0 0 0 0 0.5 12.5 i d =+++ + −+++++ = 1
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STAT0302 Business Statistics Assignment 4 () 2 22 6 6 12.5 1 1 0.9242 11 0 1 0 1 i s d r nn × =− = −× 3. (i) ± 6.1429 3.8571 yx =+ When there is an extra supermarket in a district, there are on average 3.8571 small stores more in the district. (ii) . The number of supermarket and the number of small are strongly and positively corrected. When there are more supermarkets in a district, it is very likely that there are more small stores in the district.
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This note was uploaded on 11/06/2009 for the course STAT STAT0302 taught by Professor Prof.chiu during the Spring '09 term at HKU.

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Assignment 4 suggested solution (Posted on 27 Mar) - The...

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