Question

In: Statistics and Probability

Week Sales 26 15200 27 15600 28 16400 29 15600 30 14200 31 14400 32 16400...

Week

Sales
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

The data is for weekly sales in the dry goods department at a Wal*Mart store in the Northeast.  Peak values, I.e. spikes, usually occur at holiday periods.  Week 1 is the first week of February 2002.  To show continuity, week 1 of 2003 is represented as week 54 since week 53 represents the end of fiscal 2002 and start of the 2003 fiscal year. Dollar values are adjusted in order to disguise true sales figures, but trends in the data are retained for analysis puposes.

Dry Goods

Can you identify holiday periods or special events that cause the spikes in the data?

What holiday results in the maximum sales for this department?

a) Generate linear and quadratic models for this data.

b) What is the marginal sales for this department using each model.

c) Which model do you feel best predicts future trends and explain your rational.

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

Solutions

Expert Solution

a)

Linear Model,

The regression equation is defined as,

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'y' column, Input X Range: 'x' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

Quadratic model,

The regression equation is defined as,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK.

Step 3: Select Input Y Range: 'y' column, Input X Range: 'X' column and X2 column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

b)

the marginal sales using the regression models are obtained by puuting the value of 'X' in the regreesion equation,

Linear model Quadratic model
Sales, y Week, x X^2 Y=8741.975+180.9997X Y=16889.19-164.762X+3.3569X^2
15200 26 676 13447.97 14874.65
15600 27 729 13628.97 14887.81
16400 28 784 13809.97 14907.68
15600 29 841 13990.97 14934.26
14200 30 900 14171.97 14967.55
14400 31 961 14352.97 15007.56
16400 32 1024 14533.97 15054.29
15200 33 1089 14714.97 15107.72
14400 34 1156 14895.97 15167.88
13800 35 1225 15076.97 15234.74
15000 36 1296 15257.97 15308.32
14100 37 1369 15438.97 15388.61
14400 38 1444 15619.96 15475.62
14000 39 1521 15800.96 15569.34
15600 40 1600 15981.96 15669.77
15000 41 1681 16162.96 15776.92
14400 42 1764 16343.96 15890.78
17800 43 1849 16524.96 16011.36
15000 44 1936 16705.96 16138.65
15200 45 2025 16886.96 16272.65
15800 46 2116 17067.96 16413.37
18600 47 2209 17248.96 16560.80
15400 48 2304 17429.96 16714.94
15500 49 2401 17610.96 16875.80
16800 50 2500 17791.96 17043.37
18700 51 2601 17972.96 17217.66
21400 52 2704 18153.96 17398.66
20900 53 2809 18334.96 17586.37
18800 54 2916 18515.96 17780.80
22400 55 3025 18696.96 17981.94
19400 56 3136 18877.96 18189.79
20000 57 3249 19058.96 18404.36
18100 58 3364 19239.96 18625.65
18000 59 3481 19420.96 18853.64
19600 60 3600 19601.96 19088.35
19000 61 3721 19782.96 19329.78
19200 62 3844 19963.96 19577.91
18000 63 3969 20144.96 19832.77
17600 64 4096 20325.96 20094.33
17200 65 4225 20506.96 20362.61
19800 66 4356 20687.96 20637.60
19600 67 4489 20868.96 20919.31
19600 68 4624 21049.96 21207.73
20000 69 4761 21230.96 21502.87
20800 70 4900 21411.96 21804.71
22800 71 5041 21592.96 22113.28
23000 72 5184 21773.96 22428.55
20800 73 5329 21954.96 22750.54
25000 74 5476 22135.96 23079.25
30600 75 5625 22316.96 23414.66
24000 76 5776 22497.96 23756.80
21200 77 5929 22678.96 24105.64

c)

R square for linear model = 0.670943

R square for quadratic model = 0.650563

The R square value for linear model is greater than linear model hence linear model is better fit compare to quadratic model.

The scatter plot between sales and week doesnot shows any seasonality (repeated pattern)


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