Question

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

Answer 1

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