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# Estimation of trend in time series by LSE

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Estimation of trend in Time series by method of least squares.
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#### Solution Summary

Estimation of trend in time series by method of least squares.

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## Prepare a report for the management of the Carlson Department Store that summarizes your findings, forecasts, and recommendations

Case Problem 1

The Carlson Department Store suffered heavy damage when a hurricane struck on August 31, 1996. The store was closed for four months (September 1996 through December 1996), and Carlson is now involved in a dispute with its insurance company concerning the amount of lost sales during the time the store was closed. Two key issues must be resolved: (1) the amount of sales Carlson would have made if the hurricane had not struck; and (2) whether Carlson is entitled to any compensation for excess sales from increased business activity after the storm. More than \$8 billion in federal disaster relief and insurance money came into the county, resulting in increased sales at department stores and numerous other businesses.

Table 1 Sales for Carlson Department Store, September 1992 Through August 1996

Month 1992 1993 1994 1995 1996

January 1.45 2.31 2.31 2.56
February 1.80 1.89 1.99 2.28
March 2.03 2.02 2.42 2.69
April 1.99 2.23 2.45 2.48
May 2.32 2.39 2.57 2.73
June 2.20 2.14 2.42 2.37
July 2.13 2.27 2.40 2.31
August 2.43 2.21 2.50 2.23
September 1.71 1.90 1.89 2.09
October 1.90 2.13 2.29 2.54
November 2.74 2.56 2.83 2.97
December 4.20 4.16 4.04 4.35

Table 1 shows the sales data for the 48 months preceding the storm. The U.S. Department of Commerce also published total sales for the 48 months preceding the storm for all department stores in the county, as well as the total sales in the county for the four months the Carlson Department Store was closed. Table 2 shows these data. Management has asked you to analyze these data and develop estimates of the lost sales at the Carlson Department Store for the months of September through December 1996. Management also has asked you to determine whether a case can be made for excess storm-related sales during the same period. Carlson is entitled to compensation for excess sales it would have earned in addition to ordinary sales.

Table 2 Department Store Sales for the County, September 1992 Through August 1996

Month 1992 1993 1994 1995 1996

January 46.8 46.8 43.8 48.0
February 48.0 48.6 45.6 51.6
March 60.0 59.4 57.6 57.6
April 57.6 58.2 53.4 58.2
May 61.8 60.6 56.4 60.0
June 58.2 55.2 52.8 57.0
July 56.4 51.0 54.0 57.6
August 63.0 58.8 60.6 61.8
September 55.8 57.6 49.8 47.4 69.0
October 56.4 53.4 54.6 54.6 75.0
November 71.4 71.4 65.4 67.8 85.2
December 117.6 114.0 102.0 100.2 121.8

Managerial Report

Prepare a report for the management of the Carlson Department Store that summarizes your findings, forecasts,, and recommendations. Include the following:

1. An estimate of sales had there been no hurricane.
2. An estimate of countrywide department store sales had there been no hurricane.
3. Use the countrywide actual department stores sales for September through December 1996 and the estimate in part (2) to make a case for or against excess storm related sales.
4. An estimate of lost sales for the Carlson Department Store for September through December 1996.

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