ISE 216 Question Hour Mar. 8th 2011
Q.28 Shoreline Park has kept close tabs on the number of patrons using the park since its openning in January 1993. for the first six months of operation, the following figures were recorded. Compute intercept and slope from the regression equations. What are the forecasts obtained for july through december 1993 from the regression equation. Comment on the results you obtained in part c. Month Number of Patrons Jan 133 Feb 183 Mar 285 Apr 640 May 1876 June 2550
Q. 30 For the data in problem 28, use the results of the regression equation to estimate the slope and intercept of the series at the end of june. Use these numbers as the initial values of slope and intercept required in Holt’s method. Asssume that alpha=0.15, beta=0.10 for all calculations. a) Suppose that the actual number of visitors using the park in July was 2150 and the number in august was 2660. use Holt’s method to update the estimates of the slope and imtercept based on these observations. b) What are the one step ahead and two step ahead forecasts that Holt’s method gives for the number of park visitors in september and october? ANSWER FOR PART b: One-step-ahead forecast made in Aug. for Sept. is S2 + G2 = 3525.7 Two-step-ahead forecast made in Aug for Oct is S2 + G2 = 3040 + 2(485.7) = 4011.4 c) What is the forecast made at the end of july for the number of park attendees in december?
Q. 35 A popular brand of tennis shoe has had the following demand history by quarters over a three year period. a) Using the data from 1991 to 1992, determine initial values of intercept, slope, and seasonal factors for Winter’s method. b) assume that the observed demand for the first quarter of 1993 was 18. using alpha=0.2, beta=0.15, and gamma=0.10, update the estimates of the series, the slope, and the seasonal factors. c) What are the forecasts made at the end of the first quarter 0f 1993 for the remaining three quarters? 1990 Demand 1991 1992 1 12 16 14 2 25 32 45 3 76 71 84 4 52 62 47
ANSWER 35 a) V1 = (16 + 32 + 71 + 62)/4 = 45.25 V2 = (14 + 45 + 84 + 47)/4 = 47.5 G0 = (V2 - V1)/N = 0.5625 S0 = V2 + G0 (N-1/2) = = 47.5 + (0.5625) (3/2) = 48.34 ct = Dt /(Vi[N+1/2-j]G0) where, - 2N+1 = t 0 c-7 = = 0.36, c-6 = = 0.71, c-5 = = 1.56, c-4 = = 1.35 c-3 = = 0.30, c-2 = = 0.95 c-1 = = 1.76, c0 = = 0.97 (c7 + c3)/2 = .33 (c6 + c2)/2 = .83 (c5 + c1)/2 = 1.66 (c4 + c0)/2 = 1.16 Sum = 3.98 Norming factor = 4/3.9 = 1.01 Hence the initial seasonal factors are: c-3 = .33, c-1 = 1.67, c-2 = .83, c-0 = 1.17 b) = 0.2, = 0.15, = 0.1, D1 = 18, S1 = (D1/c-3) + (1-)(S0 + G0) = 0.2(18/0.33)+0.8(48.34 + 0.56) = 50.03 G1 = (S1 - S0) + (1 - )G0 = 0.1(50.03 - 48.34) + 0.9(0.56) = 0.70 c1 = (D1/S1) + (1-)c3 = 0.15(18/50.03) + 0.85(0.33) = .3345 c) Forecasts for 2nd, 3rd and 4th quarters of 1993 F1,2 = [S1 + G1]c2 = (50 + .70)0.83 = 42.08 F1,3 = [S1 + 2G1]c3 = (50 + 2(.70))1.67 = 85.84 F1,4 = [S1 + 3G1]c4 = (50 + 3(.70))1.17 = 60.96