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Using the 911 call data in Problem 4.31, forecast calls for weeks 2 through 25 with a trend-adjusted exponential smoothing model. Assume an initial forecast for 50 calls for week 1 and an initial trend of zero. Use smoothing constants of
 = .3 and
= .2. Is this model better than that of Problem 4.31? What adjustment might be useful for further improvement? (Again, assume that actual calls in week 25 were 85.)
Emergency calls to the 911 system of Durham, North Carolina, for the past 24 weeks are shown in the following table:

a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 50 calls in the first week, and use a = .2. What is the forecast for week 25?
b) Reforecast each period using a = .6.
c) Actual calls during week 25 were 85. Which smoothing constant provides a superior forecast? Explain and justify the measure of error you used.
Storrs Cycles has just started selling the new Cyclone mountain bike, with monthly sales as shown in the table. First, co-owner Bob Day wants to forecast by exponential smoothing by initially setting February’s forecast equal to January’s sales with
 = .1. Co-owner Sherry Snyder wants to use a three-period moving average.

a) Is there a strong linear trend in sales over time?
b) Fill in the table with what Bob and Sherry each forecast for May and the earlier months, as relevant.
c) Assume that May’s actual sales figure turns out to be 405. Complete the table’s columns and then calculate the mean absolute deviation for both Bob’s and Sherry’s methods.
d) Based on these calculations, which method seems more accurate?
Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table:
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a) Graph these data to see whether a linear equation might describe the relationship between the group’s television shows and guitar sales.
b) Use the least-squares regression method to derive a forecasting equation.
c) What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month?
d) What are the correlation coefficient (
) and the coefficient of determination (
2) for this model, and what do they mean?
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