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Managerial Statistics, A Case Base Approach by: Klibanoff, Sandroni, Moselle, Saraniti

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## Managerial Statistics, A Case Base Approach by: Klibanoff, Sandroni, Moselle, Saraniti

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**1. **Summer 2009
Clayton State University
School of Business
Dr. Reza Kheirandish 1 Managerial Statistics, A Case Base Approachby: Klibanoff, Sandroni, Moselle, Saraniti

**2. **Chapter 9 Objectives:
To learn two models of seasonality
An additive model
A multiplicative model
Cases
Dada Soda
Harmon Foods (HBS)
2

**3. **Soda Sales 3 We want to forecast future sales of the magnificent Dada Soda
The data consists of quarterly sales beginning winter.

**4. **Soda Sales: Graph 4

**5. **The Data with Dummies 5

**6. **Soda Sales (cont) 6

**7. **The Regression 7

**8. **Fall Sales 8 Sales = 98817 + 6708 quarter +
5612 winter + 44590 spring + 54721 summer
Sales (Fall)= 98817 + 6708 quarter +
5612 (0) + 44590 (0) + 54721 (0)
Sales (Fall)= 98817 + 6708 quarter

**9. **Summer Sales 9 Sales = 98817 + 6708 quarter +
5612 winter + 44590 spring + 54721 summer
Sales (Summer)= 98817 + 6708 quarter +
5612 (0) + 44590 (0) + 54721 (1)
Sales (Summer)= 153538 + 6708 quarter

**10. **Difference Between Summer & Fall Sales (Fall)= 98817 + 6708 quarter
Sales (Summer)= 153538 + 6708 quarter
Expected Difference:
(153538 + 6708 quarter)-
(98817 + 6708 quarter)= 54721
Does this number look familiar? 10

**11. **Recall: The Regression 11

**12. **Multiplicative Models of Seasonality Additive models of seasonality are useful when the difference between seasons is fixed.
For instance the summer effect in Dada Soda is the same every year regardless of the base level of sales
Multiplicative models are more useful when the seasonal effect increases sales by a certain percentage.
We can see a multiplicative model at work in the Harmon Foods Case 12

**13. **Harmon Food John MacIntye, manager of Harmon Foods, wants to forecast the sales of Treat, a ready-to-eat breakfast.
The difficulty arises from the wide variability in sales. Actual sales varied from 50% to 200% of his forecast. Accurate forecasts are essential for the business.
Decide independent and dependent variables. 13

**14. **Factors Affecting Sales Caseship is the monthly average Sales of Treat measured in cases (24 packs.)
Sindexis the Seasonal Factors (one for each month)
Conpacks is the history of Consumer Packs measured in cases (24 packs).
DealAl is the actual expenditure in Dealer Allowances measured in dollars.
Competitive advertising and prices also affect sales. They are considered unpredictable and, hence, left out of the regression. 14

**15. **Consumer Packs Consumer Packs were usually a 20-cent-per-package reduction.
Sales are favorably affected during the month in which the packs were shipped.
This resulted in inventory build-ups by stores and consumers.
Hence, the consumer packs might have a negative influence in subsequent months. 15

**16. **Dealer Allowances Dealers promoted Treat by using spectacular end-of-aisle displays, ads, coupons, fliers, etc.
Much of the sales increase also lead to inventory build-ups which may last up to two months. 16

**17. **Sales of Treat (in cases) 17

**18. **Question 1 1. Using only data on monthly shipments of Treat, provide a forecast for shipments of Treat in January, 1988. Give a 95% prediction interval for this forecast. 18

**19. **Question 1 One solution is to use the average of past monthly shipments (382,522) as a forecast and then build a 95% PI around it.
Another way is to run a regression on a time index (Tindex, a variable running from 1 to 48). 19

**20. **Question 1 20

**21. **Question 1 Switch to the prediction.
Enter 49 as the value for prediction for Tindex.
Our forecast for January, 1988 is 414,137
The 95% PI is (160,089 , 668,186).
This is a wide PI !
21

**22. **Question 2 Develop and estimate a model that makes the most sense to use for forecasting monthly shipments of Treat cereal. 22

**23. **Question 2 Some of factors that we want to think about are:
time trend
the seasonal pattern of sales
the current and previous consumer pack promotions
the current and previous dealer allowances
competitors' advertising, and pricing. 23

**24. **Question 2 Competitors' behavior and pricing, are considered unpredictable. We are not informed ahead of time to use them. So, they are dropped from the regression.
We create a "de-seasonalized" shipments variable (desCases) by dividing the monthly shipments by the seasonal index (i.e., we divide January, 1984 shipments by 1.13, February, 1984 shipments by 0.98, etc.).
We create an appropriate lagged variables to capture the previous months promotions. 24

**25. **Question 2 Dependent variable:
De-seasonalized shipments.
Independent Variables:
Consumer packs
Lagged consumer packs
dealer allowances
Lagged dealer allowances
Monthly time index 25

**26. **Question 2 26

**27. **Question 2 27

**28. **Question 3 Use the model you developed above to forecast shipments for January, 1988 assuming that 200,000 consumer packs are shipped in that month and $120,000 in dealer allowances are provided. Give a 95% prediction interval for your forecast. 28

**29. **Question 3 First, we predict the deseasonalized expected number of cases shipped by plugging
200,000 for conpacks,
120,000 for DealAl,
71,881 for CP-1,
234,562 for CP-2,
552,536 for DA-1,
376,556 for DA-2, and
49 for Tindex. 29

**30. **Question 3 30

**31. **Question 3 We predict 421,758 deseasonalized cases.
Our forecast for January, 1988 is
421,758 * 1.13 = 476,587 cases of Treat.
The 95% PI is:
(345,072.7 * 1.13 , 498,443.4 * 1.13) = (389,932 , 563,241). 31

**32. **Question 4 Use your estimated model to comment on the impact/effectiveness of consumer promotions and dealer promotions. 32

**33. **Question 4 Each additional consumer pack sent out will increase deseasonalized sales of Treat by an average of 0.402 cases in that month.
But will decrease average deseasonalized sales by 0.192 next month and 0.0023 two months ahead.
The overall effect is to increase average deseasonalized sales by 0.402 - 0.192 - 0.0023 = 0.2077 cases. 33

**34. **Question 4 Each additional dollar of dealer allowances is estimated to increase average deseasonalized sales by 0.066 + 0.0066 - 0.0155 = 0.0578 cases.
Consider spending an additional dollar on dealer allowances in January.
The predicted effect is 0.066 * 1.13 + 0.0066 * 0.98 - 0.0155 * 1.02 = 0.06609 cases. 34

**35. **Question 4 1 case = 24 packs = $4.80 dollars discount. (each pack is 20 cents discount)
The 0.2077 increase in cases corresponds to 0.2077 / 4.80 = 0.04327 increase in dollars.
Dealer allowances are more effective.
35

**36. **Question 5 What improvements, if any, would you recommend to the product manager in terms of the timing and amounts of dealer promotions and consumer promotions in the future? 36

**37. **Question 5 Promotions are more effective if done in months with high seasonal indices followed by months with lower indices.
Dealer allowances seems, dollar for dollar, to be more effective than consumer packs.
November is an exception. 37

**38. **Time Series Data Regressions using time as an independent variable are likely to encounter autocorrelated residuals
This violates the assumption of independent error terms in the regression model
The fix for autocorrelation using traditional econometric analysis is called the Cochrane-Orcutt method
38

**39. **Time Series Time series analysis is another approach to dealing with time series data
This approach uses trends in time-sequenced Y variables to extrapolate forward to the next time period.
No X variables are used except for time and seasonality 39

**40. **ARIMA or Box-Jenkins The ARIMA model relies on two building blocks:
Autoregression (AR)
Moving Average (MA)
There is no theoretical model or explanation as to WHY the dependent variable ought to follow these processes
Nonetheless, ARIMA models can be useful when other information is available
40