PS4_W11_Sol

# PS4_W11_Sol - 43.47 F Apr = 38.20 F May = 29.12 2 c Compute...

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1 MS&E 261 Prof. Warren H. Hausman Winter 2010-11 SOLUTIONS TO PROBLEM SET #4 1. a) and b) Forecast Period Actual e t (86 + 75)/2 = 80.5 3 72 +8.5 (75 + 72)/2 = 73.5 4 83 -9.5 etc 77.5 5 132 -54.5 107.5 6 65 42.5 98.5 7 110 -11.5 87.5 8 90 -2.5 100.0 9 67 +33.0 78.5 10 92 -13.5 79.5 11 98 -18.5 95.0 12 73 +22.0 c) MAD = (216)/10 = 21.6 MSE = (7175)/10 = 717.5 MAPE = 100 1 n e i D i Λ Ν Μ Ξ Π Ο = 25.61 2. Using the MAD: 1.25 MAD = (1.25)(21.6) = 27.0 (Alternatively, using s, the sample standard deviation, one obtains 28.23) 3. F t = α D t-1 + (1- α )F t-1 a) F Feb = (.15)(23.3) + (.85)(25) = 24.745 F March = (.15)(72.3) + (.85)(24.745) = 31.88 F Apr = (.15)(30.3) + (.85)(31.88) = 31.64 F May = (.15)(15.5) + (.85)(31.63) = 29.22 b) F Feb = (.40)(23.3) + (.60)(25) = 24.32 F March =

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Unformatted text preview: 43.47 F Apr = 38.20 F May = 29.12 2 c) Compute MSE for February through April: Month Error (a) Error (b) ( α = .15) ( α = .40) Feb 47.45 47.88 Mar 1.56 13.17 Apr 16.13 22.70 MSE = 838.04 993.74 α = .15 gave a better forecast 4. Given information: α = .2, β = 0.2, and γ = 0.2 S 10 = 120, G 10 = 14 c 10 = 1.2 c 9 = 1.1 c 8 = 0.8 c 7 = 0.9 a) F 11 = (S 10 + G 10 )c 7 = (120 + 14)(0.9) = 120.6 b) D 11 = 128 S 11 = α (D 11 /c 7 ) + (1 - α )(S 10 + G 10 ) = 135.6 G 11 = β (S 11- S 10 ) + (1 - β )G 10 = 14.3 c 11 = γ (D 11 /S 11 ) + (1-γ )c 7 = .909 C t t = 8 11 ∑ = 4.009 The factors are normalized by multiplying each by 4/4.009 = .9978 They will not change appreciably. F 11,13 = (S 11 + 2G 11 )C 9 = (135.6 + (2)(14.3))1.1 = 180.6...
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## This note was uploaded on 02/03/2011 for the course MSANDE 261 taught by Professor -1 during the Winter '11 term at Stanford.

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PS4_W11_Sol - 43.47 F Apr = 38.20 F May = 29.12 2 c Compute...

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