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18. New car sales for a dealer in Cook County, Illinois, for the past year are shown in the following table, along with monthly indexes (seasonal relatives), which are supplied to the dealer by the regional distributor. Units Month Sold Index Jan. 640 0.SO Feb. 648 0.80 Mar. 630 0.70 Apr. 761 0.94 May 735 0.89 Jun. 850 1.00 Jul. 765 0.90 Aug. 805 1.15 Sept. 840 1.20 Oct. 828 1.20 Nov. 840 1.25 Dec. 800 1.25 a. Plot the data. Does there seem to be a trend? b. Deseasonalize car sales. c. Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs. d. Assuming no proactive approach on the part of management, discuss (no calculations necessary) how you would forecast sales for the first three months of the next year. e. What action might management consider based on your findings in part b?

User Kiven
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New car sales in Cook County show a seasonal pattern with an upward trend, and deseasonalized data reveals the need for targeted marketing and inventory management.

How is that so?

a. Plot the data. Does there seem to be a trend?

The line graph of the original data shows a slight upward trend, with sales increasing from around 640 units in January to around 800 units in December. However, there is also a clear seasonal pattern, with sales being highest in the summer and fall months and lowest in the winter and spring months.

b. Deseasonalize car sales.

To deseasonalize the car sales data, we can divide each month's sales by its corresponding monthly index. This will remove the seasonal pattern from the data, leaving us with a deseasonalized series that shows the underlying trend.

C. Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs.

The following line graph shows both the original and deseasonalized car sales data:

d. Assuming no proactive approach on the part of management, discuss (no calculations necessary) how you would forecast sales for the first three months of the next year.

To forecast sales for the first three months of the next year, we can look at the deseasonalized sales data for the corresponding months in the previous year.

The deseasonalized sales data for the first three months of the previous year are as follows:

  • January: 800
  • February: 800
  • March: 820

Based on this data, we can forecast that the dealer will sell around 800 cars in January and February of the next year, and around 820 cars in March.

However, it is important to note that this forecast is based on the assumption that there will be no major changes in the economic or competitive environment. If there are any significant changes, the forecast may need to be adjusted.

e. What action might management consider based on your findings in part b?

Based on the findings in part b, management may want to consider the following actions:

  • Increase inventory levels in the fall and winter. Since sales are highest during these months, it is important to have enough inventory on hand to meet demand.
  • Offer promotions and discounts in the spring and summer. Since sales are lowest during these months, offering promotions and discounts can help to boost sales.
  • Target marketing campaigns to different customer segments. For example, management could target families with young children during the summer months, when they are more likely to be looking for new vehicles.

18. New car sales for a dealer in Cook County, Illinois, for the past year are shown-example-1
User Tzelleke
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By identifying these patterns, the dealer can make more informed decisions regarding inventory management, marketing campaigns, and staffing levels.

Plotting the Data:

Month Units Sold Index

Jan. 640 0.80

Feb. 648 0.80

Mar. 630 0.70

Apr. 761 0.94

May. 735 0.89

Jun. 850 1.00

Jul. 765 0.90

Aug. 805 1.15

Sept. 840 1.20

Oct. 828 1.20

Nov. 840 1.25

Dec. 800 1.25

Plotting the "Units Sold" data will show the overall trend and seasonality. Plotting the "Index" data will help identify the seasonal variations within the trend.

Trend:

There appears to be a slight upward trend in car sales throughout the year, reaching a peak in December.

Seasonality:

The index data reveals a clear pattern of seasonality, with higher sales in the summer months (July-August) and lower sales in the winter months (December-February).

Deseasonalizing Car Sales

To deseasonalize car sales, we need to divide the actual sales by the corresponding index for each month. This will remove the seasonal variations and reveal the underlying trend.

Deseasonalized Sales = Actual Sales / Index

Month Deseasonalized Sales

Jan. 800

Feb. 810

Mar. 900

Apr. 808

May. 825

Jun. 850

Jul. 850

Aug. 696

Sept. 700

Oct. 690

Nov. 672

Dec. 640

Trend Analysis:

After deseasonalizing the data, the slight upward trend becomes more evident. The graph of deseasonalized sales will show a clearer picture of the underlying trend without the seasonal fluctuations.

This analysis provides valuable insights into the seasonal patterns of car sales in Cook County, Illinois. By identifying these patterns, the dealer can make more informed decisions regarding inventory management, marketing campaigns, and staffing levels.

18. New car sales for a dealer in Cook County, Illinois, for the past year are shown-example-1
User Welch
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