In: Statistics and Probability
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?
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)