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Unformatted text preview: Solutions to EndofSection and Chapter Review Problems 173 15.47 (d) The large difference between the December 2002 charges and the February 2003 cont. charges is as expected based on the monthly pattern described in (b). Coefficients Standard Error t Stat Pvalue Intercept 1.6802853 0.0226216 74.2780543 0.0000000 Coded Month 0.0061375 0.0007390 8.3049651 0.0000015 M10.1697687 0.02456606.9107258 0.0000107 M20.2308168 0.02446579.4342935 0.0000004 M30.1778855 0.02742336.4866562 0.0000205 M40.1651744 0.02725356.0606689 0.0000403 M50.1087891 0.02710284.0139468 0.0014729 M60.1178467 0.02697154.3693066 0.0007594 M70.0819297 0.02685993.0502625 0.0092953 M80.0465731 0.02676821.7398663 0.1054860 M90.0953939 0.02669673.5732450 0.0034016 M100.0495455 0.02664551.8594295 0.0857427 M110.0408071 0.02661481.5332515 0.1491835 (e) 1 2 3 4 5 6 7 8 9 10 11 ˆ log 1.6803+0.006138 0.1698 0.2308 0.1779 0.1652 0.1088 0.1178 0.08193 0.04657 0.09539 0.04955 0.04081 Y X M M M M M M M M M M M = (f) 1 log 0.0061375 b = . 0.0061375 1 10 1.01423 b = = . The estimated monthly compound growth rate is ( b 1 – 1) 100% = 1.423%. (g) 2 log 0.1697687 b =  . 0.1697687 2 10 0.67644 b = = . The January values in the time series are estimated to be on average 32.36% below the December values. (h) March of 2003: X = 26, M 3 = 1, 27 ˆ $45.9171 Y = millions (i) April of 2003: X = 27, M 4 = 1, 28 ˆ $47.9538 Y = millions (j) This classical multiplicative time series model enables the bank to predict more accurately the amount of charges on its credit cards for each of the 12 months of a year. The bank can then plan to allocate its resources more effectively to reflect the seasonal fluctuation. 15.48 (a) The retail industry is heavily subject to seasonal variation due to the holiday seasons and so are the revenues for Toys R Us. (b) 1000 2000 3000 4000 5000 6000 3 6 9 12 15 18 21 24 27 30 33 36 39 Coded Quarters Revenues There is obvious seasonal effect in the time series. 174 Chapter 15: Time Series Forecasting and Index Numbers 15.48 (c) ( 29 ( 29 ( 29 ( 29 1 2 3 ˆ 2944.3104 1.0177 0.3947 0.3901 0.4252 i X Q Q Q i Y = cont. (d) 1 log 0.007608 b = . 0.007608 1 10 1.0177 b = = . The estimated quarterly compound growth rate is ( 29 1 1 100% 1.77% b = (e) 2 log 0.4038 b =  . 0.4038 2 10 0.3947 b = = . The 1 st quarter values in the time series are estimated to be on average 60.53% below the 4 th quarter values. 3 log 0.4088 b =  . 0.4088 3 10 0.3901 b = = . The 2nd quarter values in the time series are estimated to be on average 60.99% below the 4 th quarter values. 4 log 0.3714 b =  . 0.3714 4 10 0.4252 b = = . The 3nd quarter values in the time series are estimated to be on average 57.48% below the 4 th quarter values....
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue.
 Spring '08
 Harris

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