Question

Eli Orchidhas designed a new pharmaceutical product, Orchid Relief, which improves the night sleep. Before initiating mass production of the product, Eli Orchid has been market-testing Orchid Relief in Orange County over the past 8 weeks. The daily demand values are recorded in the Excel file provided. Eli Orchid plans on using the sales data to predict sales for the upcoming week. An accurate forecast would be helpful in making arrangements for the company’s production processes and designing promotions.

Before a forecasting model is built and a forecast for the next week is generated, the COO of the company has asked the data analyst for an exploratory analysis of the demand.

Specifically, the COO has asked the analyst[1]:

To provide a bar/column chart (with data labels rounded to two decimal points) showing the average demand for each day of the week (Sun., Mon., etc.)	[add chart here]
To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2	d = R2=
To fit a multiple regression model with a dummy variable representing the weekend, and to provide the regression equation (d = a*t + b*w + c), along with Adjusted R2.	d = Adjusted R2=
To provide a line graph of the actual demand with a simple regression and multiple a regression overlay.	[add chart here]
To write a short paragraph explaining the observations and providing general recommendations. Specifically: Provide interpretation of all the numbers (e.g. R^2, coefficients, etc.) Evaluate both models. Can they be used for prediction (use the pvalues from the regression output)? Explain. Compare the models and explain which one should be used. Why? Provide general recommendations for the next sevenday demand forecast. Make sure you use proper terminology. Points will be taken for not using the appropriate terms to describe your observations. Note: this paragraph can be on page 2. The answers to previous questions must all fit on the first page.	[write your paragraph here]

[1]Round numbers to four decimal points (e.g. 0.1234), unless explicitly requested otherwise.

Day	Date	Weekday	Daily Demand	Weekend
1	4/25/16	Mon	297	0
2	4/26/16	Tue	293	0
3	4/27/16	Wed	327	0
4	4/28/16	Thu	315	0
5	4/29/16	Fri	348	0
6	4/30/16	Sat	447	1
7	5/1/16	Sun	431	1
8	5/2/16	Mon	283	0
9	5/3/16	Tue	326	0
10	5/4/16	Wed	317	0
11	5/5/16	Thu	345	0
12	5/6/16	Fri	355	0
13	5/7/16	Sat	428	1
14	5/8/16	Sun	454	1
15	5/9/16	Mon	305	0
16	5/10/16	Tue	310	0
17	5/11/16	Wed	350	0
18	5/12/16	Thu	308	0
19	5/13/16	Fri	366	0
20	5/14/16	Sat	460	1
21	5/15/16	Sun	427	1
22	5/16/16	Mon	291	0
23	5/17/16	Tue	325	0
24	5/18/16	Wed	354	0
25	5/19/16	Thu	322	0
26	5/20/16	Fri	405	0
27	5/21/16	Sat	442	1
28	5/22/16	Sun	454	1
29	5/23/16	Mon	318	0
30	5/24/16	Tue	298	0
31	5/25/16	Wed	355	0
32	5/26/16	Thu	355	0
33	5/27/16	Fri	374	0
34	5/28/16	Sat	447	1
35	5/29/16	Sun	463	1
36	5/30/16	Mon	291	0
37	5/31/16	Tue	319	0
38	6/1/16	Wed	333	0
39	6/2/16	Thu	339	0
40	6/3/16	Fri	416	0
41	6/4/16	Sat	475	1
42	6/5/16	Sun	459	1
43	6/6/16	Mon	319	0
44	6/7/16	Tue	326	0
45	6/8/16	Wed	356	0
46	6/9/16	Thu	340	0
47	6/10/16	Fri	395	0
48	6/11/16	Sat	465	1
49	6/12/16	Sun	453	1
50	6/13/16	Mon	307	0
51	6/14/16	Tue	324	0
52	6/15/16	Wed	350	0
53	6/16/16	Thu	348	0
54	6/17/16	Fri	384	0
55	6/18/16	Sat	474	1
56	6/19/16	Sun	485	1

Answer 1

Sol 1:

  

Sol 2:

Required Equation: d = 1.0356 t + 339.29 ( a = 1.0356, b = 339.29)
R² = 0.0761

Sol 3:

d = a*t + b*w + c

Required Equation: d = 0.679326655 t + 116.3916428 w + 316.5492309

( a = 0.679326655, b = 116.3916428, c = 316.5492309 )

Adjusted R² = 0.815695457

Sol 4:

Sol 5:

As we can see from the above graph, Linear regression model is a trend line which does not take into account the seasonality factor. On the other hand, multiple regression model prediction is much better as compared to linear regression as it can predict more accurately and includes the seasonality factor as well.