Eli Orchid has 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]:

1. To provide a bar chart (with data labels rounded to two decimal points) showing the average demand for each week day (Sun., Mon., etc.)

[add chart here]

2. To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R²

d =

R²=

3. 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 R².

d =

Adjusted R²=

4. To provide a run-series plot of the actual demand with simple regression and multiple regression overlay.

[add chart here]

5. To write a short paragraph explaining the observations and providing general recommendations for the next seven days demand forecast.

[write your paragraph here]

6. To fit a new multiple regression model with dummy variables for seven days in a week (Mon, Tue, ..., Sun), and to provide the regression equation (d = a*t + b₁x₁ + b₂x₂ + b₃x₃ + b₄x₄ + b₅x₅ + b₆x₆ + c), along with R².

d =

R²=

7. To use all three models:

M1: d = 1.0356t + 339.29

M2: d=0.7163t+116.7679w+315.0262

M3: (the one considering weekdays)

to predict the demand for seven days ahead (Mon, Tue, ..., Sun) and find the total weekly demand.

M1

M2

M3

Mon.

Tue.

Wed.

Thu.

Fri.

Sat.

Sun.

TOTAL:

8. Take advantage of the fact that new demand data became available and use this new data to compare the forecasts using MAPE for days 57-63.

New: M: 311 T: 341 W: 357 Th: 363 F: 390 Sa: 490 Su: 492

MAPE_M1:

MAPE_M2:

MAPE_M3:

9. To provide a line chart with the actual demand (including the new data) and M2 and M3.

10. To choose the best model for forecasting daily demand at Orchid Relief for 7 days ahead and write a short paragraph explaining your choice.

[write your paragraph here]

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

Excel Data Info Shown below:

39 38 6/1/2016 Wed 333 40 39 6/2/2016 Thu 339 41 40 6/3/2016 Fri 416 42 41 6/4/2016 Sat 475 43 42 6/5/2016 Sun 459 44 43 6/6/2016 Mon 319 45 44 6/7/2016 Tue 326 46 45 6/8/2016 Wed 356 47 46 6/9/2016 Thu 340 48 47 6/10/2016 Fri 395 49 48 6/11/2016 Sat 465 50 49 6/12/2016 Sun 453 51 50 6/13/2016 Mon 307 52 51 6/14/2016 Tue 324 53 52 6/15/2016 Wed 350 54 53 6/16/2016 Thu 348 55 54 6/17/2016 Fri 384 56 55 6/18/2016 Sat 474 57 56 6/19/2016 Sun 485E2 X =IF(OR($C2="Sat",$C2="Sun"),1,0) A B C D E F G H Day Date Weekday Daily Demand Weekend 2 1 4/25/2016 Mon 297 0 3 2 4/26/2016 Tue 293 0 Check the formula 4 3 4/27/2016 Wed 327 5 4 4/28/2016 Thu 315 6 5 4/29/2016 Fri 348 7 6 4/30/2016 Sat 147 8 7 5/1/2016 Sun 431 9 8 5/2/2016 Mon 283 10 9 5/3/2016 Tue 326 11 10 5/4/2016 Wed 317 12 11 5/5/2016 Thu 345 12 5/6/2016 Fri 355 14 13 5/7/2016 Sat 428 15 14 5/8/2016 Sun 454 16 15 5/9/2016 Mon 305 17 16 5/10/2016 Tue 310 19 17 5/11/2016 Wed 350 ic 18 5/12/2016 Thu 308 20 19 5/13/2016 Fri 366 21 20 5/14/2016 Sat 460 22 21 5/15/2016 Sun 427 23 22 5/16/2016 Mon 291 24 23 5/17/2016 Tue 325 25 24 5/18/2016 Wed 354 26 25 5/19/2016 Thu 322 27 26 5/20/2016 Fri 405 28 27 5/21/2016 Sat 442 29 28 5/22/2016 Sun 454 30 29 5/23/2016 Mon 318 31 30 5/24/2016 Tue 298 32 31 5/25/2016 Wed 355 33 32 5/26/2016 Thu 355 34 33 5/27/2016 Fri 374 35 34 5/28/2016 Sat 447 36 35 5/29/2016 Sun 463 37 36 5/30/2016 Mon 291 38 37 5/31/2016 Tue 319