Assignment 5 sol

# Assignment 5 sol - The University of Hong Kong Department...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT0302 Business Statistics Semester 2 2008/2009 Assignment 5 Suggested Solution 1. (a) Consider the following two data sheets (1) (2) (3) (4) (5) (6) (7) (8) Year Quarter i y .. M A i y MA S i x i t 2005 1 9.8 N.A. N.A. 0.8644 1 11.3370 2 15.3 N.A. N.A. 1.3162 2 11.6242 3 13.5 12.6125 1.0704 1.0403 3 12.9772 4 10.4 13.5125 0.7697 0.7791 4 13.3492 2006 1 12.7 14.2875 0.8889 0.8644 5 14.6919 2 19.6 14.8750 1.3176 1.3162 6 14.8912 3 15.4 15.4500 0.9968 1.0403 7 14.8037 4 13.2 16.0125 0.8244 0.7791 8 16.9432 2007 1 14.5 16.7375 0.8663 0.8644 9 16.7742 2 22.3 17.1500 1.3003 1.3162 10 16.9425 3 18.5 17.3000 1.0694 1.0403 11 17.7836 4 13.4 17.7500 0.7549 0.7791 12 17.1999 2008 1 15.5 18.2125 0.8511 0.8644 13 17.9310 2 24.9 18.4375 1.3505 1.3162 14 18.9178 3 19.6 N.A. N.A. 1.0403 15 18.8410 4 14.1 N.A. N.A. 0.7791 16 18.0984 Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 2005 N.A. N.A. 1.0704 0.7697 2006 0.8889 1.3176 0.9968 0.8244 2007 0.8663 1.3003 1.0694 0.7549 2008 0.8511 1.3505 N.A. N.A. Total Mean 0.8688 1.3228 1.0455 0.7830 4.0201 S 0.8644 1.3162 1.0403 0.7791 4 Adjust the seasonal pattern by () ( ) Term Total 4 Mean Term Mean Total 4.0201 Si S i == where number of terms. Mean Total = The seasonal factors are 0.8644, 1.3162, 1.0403 and 0.7791 for Quarters 1 to 4 respectively. (b) 11.5680 0.5001 i i tx =+ ± 1

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STAT0302 Business Statistics Assignment 5 (c) Forecasting 2009 i x i T S ± i i y TS = × 1 17 20.0702 0.8644 17.3492 2 18 20.5703 1.3162 27.0751 3 19 21.0705 1.0403 21.9193 4 20 21.5706 0.7791 16.8051 The sales volumes of the four quaters in 2009 are forecasted to be 17.3492, 27.0751, 21.9193 and 16.8051 respectively Remarks: rounding errors can be severe when using the calculator. The answers above were obtained by Excel with a high accuracy. In each step, numbers of at least 4 significance figures is required to yield the accurate solution. 2. (a) Consider the following two data sheets (1) (2) (3) (4) (5) (6) (7) (8) Year Term i y .. M A i y MA S i x i t 2006 1 5.5 N.A. N.A. 0.9135 1 6.0209 2 6.8 N.A. N.A. 1.0557 2 6.4412 3 8 N.A. N.A. 1.1408 3 7.0124 4 7.4 6.6583 1.1114 1.1085 4 6.6759 5 5.9 6.7750 0.8708 0.8615 5 6.8488 6 6 6.8500 0.8759 0.9201 6 6.5214 2007 1 6.2 6.9583 0.8910 0.9135 7 6.7872 2 7.5 7.1250 1.0526 1.0557 8 7.1043 3 8.2 7.3667 1.1131 1.1408 9 7.1877 4 8.5 7.6833 1.1063 1.1085 10 7.6683 5 6.8 7.9750 0.8527 0.8615 11 7.8936 6 8 8.2917 0.9648 0.9201 12 8.6952 2008 1 8 8.5417 0.9366 0.9135 13 8.7577 2 9.2 8.6833 1.0595 1.0557 14 8.7146 3 10.3 8.8083 1.1693 1.1408 15 9.0284 4 9.4 N.A. N.A. 1.1085 16 8.4802 5 7.6 N.A. N.A. 0.8615 17 8.8222 6 8.7 N.A. N.A. 0.9201 18 9.4560 Year Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 2006 N.A. N.A. N.A. 1.1114 0.8708 0.8759 2007 0.8910 1.0526 1.1131 1.1063 0.8527 0.9648 2008 0.9366 1.0595 1.1693 N.A. N.A. N.A. Total Mean 0.9138 1.0561 1.1412 1.1088 0.8618 0.9204 6.0021 S 0.9135 1.0557 1.1408 1.1085 0.8615 0.9201 6.0000 Adjust the seasonal pattern by 2
STAT0302 Business Statistics Assignment 5 () ( ) Term Total 6 Mean Term Mean Total 6.0021 Si S i == where number of terms. Mean Total = The bimonthly seasonal indexes are 0.9135, 1.0557, 1.1408, 1.1085, 0.8615 and 0.9201 for Terms 1 to 6 respectively. (b) 5.8701 0.1898 i i tx =+ ± (c) Forecasting 2009 i x i T S ± i i y TS = × 1 19 9.4761 0.9135 8.6563 2 20 9.6659 1.0557 10.2043 3 21 9.8557 1.1408 11.2438 4 22 10.0455 1.1085 11.1350 5 23 10.2353 0.8615 8.8173 6 24 10.4251 0.9201 9.5916 The sales of the coming six issues in 2009 are forecasted to be 8.6563, 10.2043, 11.2438, 11.1350, 8.8173 and 9.5916 respectively Remarks: rounding errors can be severe when using the calculator. The answers above were obtained by Excel with a high accuracy. In each step, numbers of at least 4 significance figures is required to yield the accurate solution. 3. (a) Consider the following two data sheets (1) (2) (3) (4) (5) (6) (7) (8) Year Term i y .. M A i y MA S i x i t 2005 1 9.6 N.A. N.A. 0.8419 1 11.4032 2 14.4 12.0 1.2000 1.1939 2 12.0618 3 12.0 12.6 0.9524 0.9643 3 12.4446 2006 1 11.4 13.4 0.8507 0.8419 4 13.5412 2 16.8 14.0 1.2000 1.1939 5 14.0721 3 13.8 14.4 0.9583 0.9643 6 14.3113 2007 1 12.6 15.0 0.8400 0.8419 7 14.9666 2 18.6 15.7 1.1847 1.1939 8 15.5798 3 15.9 16.2 0.9815 0.9643 9 16.4891 2008 1 14.1 16.9 0.8343 0.8419 10 16.7484 2 20.7 17.4 1.1897 1.1939 11 17.3388 3 17.4 N.A. N.A. 0.9643 12 18.0446 Year T e r m 1T e r m 2T e r m 3 2005 N.A. 1.2000 0.9524 2006 0.8507 1.2000 0.9583 2007 0.8400 1.1847 0.9815 3

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STAT0302 Business Statistics Assignment 5 2008 0.8343 1.1897 N.A. Total Mean 0.8417 1.1936 0.9641 2.9993 S 0.8419 1.1939 0.9643 3 Adjust the seasonal pattern by () ( ) Term Total 3 Mean Term Mean Total 2.9993 Si S i == where number of terms. Mean Total = The seasonal factors are 0.8419, 1.1939 and 0.9643 for Terms 1 to 3 respectively.
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Assignment 5 sol - The University of Hong Kong Department...

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