Question

In: Statistics and Probability

Orchard Relief is a product that is designed to improve sleep at night. The company, Eli...

Orchard Relief is a product that is designed to improve sleep at night. The company, Eli Orchard, is guessing that sales of the product is somewhat related to sleeping patterns of customers over the days of the week. Before mass production of the product, Eli Orchid has market-tested Orchid Relief in only Orange County over the past 8 weeks. The weekly demand is recorded. Eli Orchid is now trying to use the sales pattern over the past 8 weeks to predict sales in US for the upcoming few weeks, especially for days 57 and 60. An accurate forecast would be helpful in arrangements for the company’s production processes and design of price promotions over each week.

Using the regression method on the de-seasonalized time series, what is a de-seasonalized forecast for day 60?

Number of Days Daily Demand
1 297
2 293
3 327
4 315
5 348
6 447
7 431
8 283
9 326
10 317
11 345
12 355
13 428
14 454
15 305
16 310
17 350
18 328
19 366
20 460
21 427
22 291
23 325
24 354
25 322
26 405
27 442
28 450
29 318
30 298
31 355
32 355
33 374
34 447
35 463
36 291
37 319
38 333
39 339
40 416
41 475
42 459
43 319
44 326
45 356
46 340
47 395
48 465
49 453
50 307
51 324
52 350
53 348
54 384
55 474
56 485

Solutions

Expert Solution

for day 57 the demand will be 399 and for day 60 the demand will be 402

the simple linear regression model is Demand(y)=a+bt=339.9805+1.0314*day(t)

for t=60, the y=339.9805+1.0314*60=401.8645 ( next whole number is 402)

for  t=60, the y=339.9805+1.0314*57=399.7703 ( next whole number is 399)

following regression analysis information has been generated using ms-excel

Regression Statistics
Multiple R 0.273964
R Square 0.075056
Adjusted R Square 0.057928
Standard Error 59.01583
Observations 56
ANOVA
df SS MS F Significance F
Regression 1 15261.68 15261.68 4.381927 0.041034
Residual 54 188074.9 3482.868
Total 55 203336.6
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 339.9805 15.98628 21.26702 6.5E-28 307.93 372.0311
t 1.02136 0.487917 2.093305 0.041034 0.043145 1.999576

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