Spreadsheet Modeling & Decision Analysis: A Practical Introduction To Business Analytics, Loose-leaf Version
8th Edition
ISBN: 9781337274852
Author: Ragsdale, Cliff
Publisher: South-Western College Pub
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The following time series represents the number of automobiles sold by a car dealership each of the past five months.
t
1
2
3
4
5
Yt
7
12
10
13
14
(a) Construct a time series plot.
What type of pattern exists in the data?
The time series plot shows a linear trend.The time series plot shows a horizontal pattern. The time series plot shows a seasonal pattern.The time series plot shows a nonlinear trend.
(b)
Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
t =
(c)
What is the forecast for
t = 6?
A cyclical pattern will depict a systematic increase or decrease in the mean of time series data and over time.
A pharmacist has been monitoring sales of a certain over-the-counter pain reliever. Daily sales during the last 15 days were as follows:Day 1 2 3 4 5 6 7 8 9Number sold 36 38 42 44 48 49 50 49 52Day 10 11 12 13 14 15Number sold 48 52 55 54 56 57a. Which method would you suggest using to predict future sales—a linear trend equation or trend-adjusted exponential smoothing? Why?
b. If you learn that on some days the store ran out of the specific pain reliever, would that knowledge cause you any concern? Explain
c. Assume that the data refer to demand rather than sales. Using trend-adjusted smoothing with an initial forecast of 50 for day 8, an initial trend estimate of 2, and α = β = .3, develop forecasts for days 9 through 16. What is the MSE for the eight forecasts for which there are actual data?
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- Management of a home appliance store wants to understand the growth pattern of the monthly sales of a new technology device over the past two years. The managers have recorded the relevant data in the file P13_05.xlsx. Have the sales of this device been growing linearly over the past 24 months? By examining the results of a linear trend line, explain why or why not.arrow_forwardThe file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use Holts method with optimized smoothing constants. b. Which of these two methods appears to provide the best forecasts? Answer by comparing their MAPE values.arrow_forwardThe file P13_28.xlsx contains monthly retail sales of U.S. liquor stores. a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters method to forecast this series with smoothing constants = = 0.1 and = 0.3. Does the forecast series seem to track the seasonal pattern well? What are your forecasts for the next 12 months?arrow_forward
- The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?arrow_forwardThe file P13_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month and will continue to do so for at least the near future. a. Explain briefly whether the plot of the series visually supports the companys suspicion. b. By what percentage are sales increasing each month? c. What is the MAPE for the forecast model in part b? In words, what does it measure? Considering its magnitude, does the model seem to be doing a good job? d. In words, how does the model make forecasts for future months? Specifically, given the forecast value for the last month in the data set, what simple arithmetic could you use to obtain forecasts for the next few months?arrow_forwardThe management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.arrow_forward
- The file P13_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b?arrow_forwardA small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?arrow_forwardThe file P13_25.xlsx contains the quarterly numbers of applications for home mortgage loans at a branch office of Northern Central Bank. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b? Is it guaranteed to produce better forecasts for the future?arrow_forward
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