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Quantitative Methods for Business Study Set 1
Quiz 6: Forecasting
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Question 41
Essay
A trend line for the attendance at a restaurant's Sunday brunch is given by Number = 264 + .72(t) How many guests would you expect in week 20?
Question 42
Essay
Use the following to forecast a value for period 14,a second quarter. T = 16.32 - .18(t) C
2
= .91 S
2
= .75
Question 43
Essay
Quarterly billing for water usage is shown below.
a.Find the seasonal index for each quarter. b.Deseasonalize the data. c.Find the trend line. d.Assume there is no cyclical component and forecast the summer billing for year 5.
Question 44
Essay
Connie Harris,in charge of office supplies at First Capital Mortgage Corp. ,would like to predict the quantity of paper used in the office photocopying machines per month.She believes that the number of loans originated in a month influence the volume of photocopying performed.She has compiled the following recent monthly data:
a.Develop the least-squares estimated regression equation that relates sheets of photocopy paper used to loans originated. b.Use the regression equation developed in part (a)to forecast the amount of paper used in a month when 65 loan originations are expected.
Question 45
Essay
Sales (in thousands)of the new Thorton Model 506 convection oven over the eight-week period since its introduction have been as follows:
a.Which exponential smoothing model provides better forecasts,one using SYMBOL 97 \f "Symbol" = .6 or
α
\alpha
α
= .2? Compare them using mean squared error. b.Using the two forecast models in part (a),what are the forecasts for week 9?
Question 46
Essay
The number of girls who attend a summer basketball camp has been recorded for the seven years the camp has been offered.Use exponential smoothing with a smoothing constant of .8 to forecast attendance for the eighth year. 47,68,65,92,98,121,146
Question 47
Essay
In order to forecast the attendance at an annual tennis tournament,a model has been developed which uses attendance from the previous year and the amount spent for advertising this year.From the years shown in the table,forecast the attendance for years 2-5 and calculate the forecast error.
The multiple regression model is Attendance = 6738 + .23($)+ .25 (Attlag)
Question 48
Essay
Monthly sales at a coffee shop have been analyzed.The seasonal index values are
and the trend line is 74123 + 26.9(t).Assume there is no cyclical component and forecast sales for year 8 (months 97 - 108).
Question 49
Essay
Quarterly revenues (in $1,000,000's)for a national restaurant chain for a five-year period were as follows:
a.Determine the appropriate seasonal index values for this time series. b.Determine the appropriate trend value for this time series. c.Forecast the revenues for the next four quarters.
Question 50
Essay
The number of cans of soft drinks sold in a machine each week is recorded below.Develop forecasts using a three period moving average. 338,219,278,265,314,323,299,259,287,302
Question 51
Essay
The number of plumbing repair jobs performed by Auger's Plumbing Service in each of the last nine months are listed below.
a.Assuming a linear trend function,forecast the number of repair jobs Auger's will perform in December using the least squares method. b.What is your forecast for December using a three-period weighted moving average with weights of .6,.3,and .1? How does it compare with your forecast from part (a)?
Question 52
Essay
Use a four period moving average to forecast attendance at baseball games.Historical records show 5346,7812,6513,5783,5982,6519,6283,5577,6712,7345
Question 53
Essay
Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1)Christmas (November-December); (2)Father's Day (late May - mid-June);and (3)all other times.Average weekly sales (in $'s)during each of these three seasons during the past four years has been as follows:
Determine a forecast for the average weekly sales in year 5 for each of the three seasons.
Question 54
Essay
The average SAT verbal score for students from one high school over the last ten exams is 508,490,502,505,493,506,492,490,503,501 Do the scores support an increasing or a decreasing trend?
Question 55
Essay
The number of properties newly listed with a real estate agency in each quarter over the last four years is given.Calculate the seasonal index values.
Question 56
Essay
A 24-hour coffee/donut shop makes donuts every eight hours.The manager must forecast donut demand so that the bakers have the fresh ingredients they need.Listed below is the actual number of glazed donuts (in dozens)sold in each of the preceding 13 eight-hour shifts.
Forecast the demand for glazed donuts for the three shifts of June 8 and the three shifts of June 9.
Question 57
Essay
The number of pizzas ordered on Friday evenings between 5:30 and 6:30 at a pizza delivery location for the last 10 weeks is shown below.Use exponential smoothing with smoothing constants of .2 and .8 to forecast a value for week 11.Compare your forecasts using MSE.Which smoothing constant would you prefer? 58,46,55,39,42,63,54,55,61,52
Question 58
Essay
A hospital records the number of floral deliveries its patients receive each day.For a two week period,the records show 15,27,26,24,18,21,26,19,15,28,25,26,17,23 Use exponential smoothing with a smoothing constant of .4 to forecast the number of deliveries.
Question 59
Essay
The number of new contributors to a public radio station's annual fund drive over the last ten years is 63,58,61,72,98,103,121,147,163,198 Develop a trend equation for this information,and use it to predict next year's number of new contributors.