Question

In: Statistics and Probability

The WalMart’s fiscal year starts the first week of February. This means that when analyzing the...

The WalMart’s fiscal year starts the first week of February. This means that when analyzing the data, week 26 is actually week 30 (26+4 weeks for January) in 2002 or the end of July 2002. Also, week 52 is actually week 4 (52+4 weeks for January 2002 minus 52 weeks for 2002) in 2003 or the end of January 2003. As an example, the spike in sales (revenue) at week 75 occurs in week 27 (75+4 weeks for January 2002 minus 52 weeks for 2002) in 2003 or the first week in July 2003. This corresponds to sales for the July 4th holiday when people are buying barbecue related items. Please use excel.

Week Sales in $
26 15200
27 15600
28 16400
29 15600
30 14200
31 14400
32 16400
33 15200
34 14400
35 13800
36 15000
37 14100
38 14400
39 14000
40 15600
41 15000
42 14400
43 17800
44 15000
45 15200
46 15800
47 18600
48 15400
49 15500
50 16800
51 18700
52 21400
53 20900
54 18800
55 22400
56 19400
57 20000
58 18100
59 18000
60 19600
61 19000
62 19200
63 18000
64 17600
65 17200
66 19800
67 19600
68 19600
69 20000
70 20800
71 22800
72 23000
73 20800
74 25000
75 30600
76 24000
77 21200

Identify spikes (outliers) in the data where extreme sales values occur and correlate these spikes with actual calendar dates in 2002 or 2003 and with holidays or special events that may occur during these periods.

1. Modeling the data linearly - a. Generate a linear model for this data by choosing two points.

b. Generate a least squares linear regression model for this data.

c. How good is this regression model? Output and discuss the R2 value.

d. What are the marginal sales (derivative, i.e. rate of change) for this department using the linear model with two data points and the regression model?

e. Compare the two models. Which do you feel is better?

f. Remove appropriate outliers as you deem necessary and rerun the linear regression model. What is the marginal sales and discuss improvements.

2. Modeling the data quadratically - a. Generate a quadratic model for this data. Also output and discuss the R2 value.

b. What are the marginal sales for this department using this model?

c. Calculate the model generated relative max/min value. Show backup analytical work.

d. Compare actual and model generated relative max/min value.

e. Remove outliers and rerun the quadratic least squares model. What is the marginal sales and discuss improvements.

3. Comparing models - a. Based on all models run, which model do you feel best predicts future trends? Explain your rationale.

b. Based on the model selected, what type of seasonal adjustments, if any, would be required to meet customer needs?

Solutions

Expert Solution

Since 1st question has four sub questions, I'm answering the 1st one

1. Holidays or special events could be either increases or decreases. They do not necessarily have to be recurring. If it is recurring, then the same effect will be applied to every instance. You can have a one-time holiday, which would effectively allow the model to fit any one-time spikes without affecting the future at all.

If we identified outliers, it is better to remove them from the historical data then to fit them as one-time holidays or special events. That is because every holiday or special events introduces an additional parameter into the model, and so fitting and predicting will become slower with no benefit over just removing the points.

In the data where extreme sales values occcur and correlate these soikes with actual calender dates in 2002 or 2003 and with holidays or special events that may occur during these periods spikes is 23. Because the holidays or special events not taken as outliers. At week 75 occurs in week 27(75+4 weeks for January 2002 minus 52 weeks for 2002) in 2003 or the first week in July 2003. This corresponds to sales for the July 4th holiday when people are buying barbecue related items. 27-3 = 23 outliers.

In the data where extreme sales values occcur and correlate these soikes with actual calender dates in 2002 or 2003 and with holidays or special events that may occur during these periods spikes is 23.


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