1. The following data shows the value of food and beverage sales ($1,000s) for the first three years of operation of Vintage Restaurant on Captiva Island near Fort Myers, Florida.

Month	First Year	Second Year	Third Year
January	242	263	282
February	235	238	255
March	232	247	265
April	178	193	205
May	184	193	210
June	140	149	160
July	145	157	166
August	152	161	174
September	110	122	126
October	130	130	148
November	152	167	173
December	206	230	235

1. Compute the seasonal indexes
2. Which month has the largest change in the value of food and beverage sales?
3. Use 3-mth moving average to forecast the value of food and beverage sales for January of the fourth year.
4. Use exponential smoothing model to forecast the value of food and beverage sales for January of the fourth year. Assume a smoothing constant of 0.10.
5. Use the trend projection model to forecast the value of food and beverage sales for January of the fourth year.
6. Compare the three forecast methods you have used and recommend the forecast for Winter of 2022.
7. Discuss the results of the trend projection model for this problem.

2.

Month	Sales
January	20
February	21
March	15
April	14
May	13
June	16
July	17
August	18
September	20
October	20
November	21
December	23

The monthly sales for Yazici Batteries, Inc., were as shown in the above table.

1. Forecast January sales of the coming year using each of the following:
   1. Nave method
   2. 4-mth moving average
   3. Exponential smoothing using an alpha = 0.25
   4. A trend projection model
2. With the data given, which method would you recommend for this data set and why?
3. Discuss the trend projection model that you obtained for this data set.

3.

A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

1. Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, systolic blood pressure, and whether the person is a smoker.

Risk	Age	Pressure	Smoker
12	57	152	No
24	67	163	No
13	58	155	No
56	86	177	Yes
28	59	196	No
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
37	59	207	Yes

1. Is smoking a significant factor in the risk of stroke? Explain. Use a 0.05 level of significance.
2. What is the probability of a stroke over the next 10 years for Art Speen, a 68-year old smoker who has a systolic blood pressure of 175? What action might the physician recommend for this patient?

4.

Johnson Filtration, Inc. provides maintenance service for water filtration systems throughout Southern Florida. Customers contact Johnson with requests for maintenance service on their water filtration systems. To estimate service time and the service cost, Johnson's managers want to predict the repair time necessary for each maintenance request. Hence, repair time in hours is the dependent variable. Repair time is believed to be related to three factors: the number of months since the last maintenance service, the type of repair problem (mechanical or electrical), and the repairperson who performs the repair (Donna Newton or Bob Jones). Data for a sample of 10 service calls are reported in the following table:

Repair Time in Hours	Months Since Last Service	Type of Repair	Repairperson
2.9	2	Electrical	Donna Newton
3.0	6	Mechanical	Donna Newton
4.8	8	Electrical	Bob Jones
1.8	3	Mechanical	Donna Newton
2.9	2	Electrical	Donna Newton
4.9	7	Electrical	Bob Jones
4.2	9	Mechanical	Bob Jones
4.8	8	Mechanical	Bob Jones
4.4	4	Electrical	Bob Jones
4.5	6	Electrical	Donna Newton

1. Develop the multiple regression equation to predict repair time, given the number of months since the last maintenance service, the repairperson and the type of repair.
2. What are the interpretations of the estimated regression parameters?
3. What does the coefficient of determination tell you about this model?

5.

Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are shown for the past 12 weeks:

Week	1	2	3	4	5	6	7	8	9	10	11	12
Actual Passenger Miles (in thousands)	17	21	19	23	18	16	20	18	22	20	15	22

1. Assuming an initial forecast for week 1 of 17,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use a smoothing constant of 0.2.
2. Present a table to compute the Tracking Signal for this problem.
3. Develop a Control Chart of the Tracking Signal using a control limit of +2.5 MAD.
4. For the forecast to be in control, what percentage of the errors must fall within + 2.5 MAD?
5. Is this forecast in control? Explain.