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?

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)

orchestra answered 2 years ago

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