Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table: Demand for Guitars 3 6 7 5 10 7 Maroon 5 TV Appearances 3 4 7 6 8 5 Graph these data to see whether a linear equation might describe the relationship between the group’s television shows and guitar sales. Use the least-squares regression method to derive a forecasting equation. Use the least-squares regression method to derive a forecasting equation. What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month? Weekly sales of copy paper at Cubicle Suppliers are provided in the table below. Compute a three-period moving average and a four-period moving average for weeks 5, 6, and 7. Compute the MAD for both forecasting methods. Which model is more accurate? Forecast week 8 with the more accurate method. Week Sales (cases) 1 17 2 21 3 27 4 31 5 19 6 17 7 21 Answer Week Sales (cases) 3MA |error| 4MA |error| 1 17 2 21 3 27 4 31 5 19 6 17 7 21 8 Sales for refrigerators are given in the table below. Using a 3-month moving average, forecast sales for February the following year. Calculate the MAD for this model. 3-Month Absolute Month Sales Moving Average Deviation January 11 February 14 March 16 April 10 May 15 June 17 July 11 August 14 September 17 October 12 November 14 December 16 January 11 February Use the weighted moving average to forecast sales for February the following year . Calculate the MAD for this model. Which model is better? Month Sales 3-Month Weighted Moving Average Absolute Deviation January 11 February 14 March 16 April 10 May 15 June 17 July 11 August 14 September 17 October 12 November 14 December 16 January 11 February Lillian Sam, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Sam has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year: Crime Patients Year Rate X Y 1 58.3 36 2 61.1 33 3 73.4 40 4 75.7 41 5 81.1 40 6 89.0 55 7 101.1 60 8 94.8 54 9 103.3 58 10 116.2 61 Column totals 854.0 478 Using trend (linear regression) analysis, predict the number of patients Dr. Sam will see in years 11 and 12 as a function of time. The following gives the number of pints of type B blood used at Woodlawn Hospital in the past 6 weeks: Week of Pints used August 31 360 September 7 389 September 14 410 September 21 381 September 28 368 October 5 374 October 12 Forecast the demand for the week of October 12 using Sales of Volkswagen’s popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). The sales manager had predicted before the new model was introduced that first year sales would be 410 VWs. Using exponential smoothing with a weight of α =.30, develop forecasts for years 2 through 6. Forecast Exponential Absolute Year Sales Smoothing a = 0.6 Deviation 1 450 410.0 2 495 3 518 4 563 5 584 6 Forecast Exponential Absolute Year Sales Smoothing a = 0.9 Deviation 1 450 410.0 2 495 3 518 4 563 5 584 6

Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table: Demand for Guitars 3 6 7 5 10 7 Maroon 5 TV Appearances 3 4 7 6 8 5 Graph these data to see whether a linear equation might describe the relationship between the group’s television shows and guitar sales. Use the least-squares regression method to derive a forecasting equation. Use the least-squares regression method to derive a forecasting equation. What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month? Weekly sales of copy paper at Cubicle Suppliers are provided in the table below. Compute a three-period moving average and a four-period moving average for weeks 5, 6, and 7. Compute the MAD for both forecasting methods. Which model is more accurate? Forecast week 8 with the more accurate method. Week Sales (cases) 1 17 2 21 3 27 4 31 5 19 6 17 7 21 Answer Week Sales (cases) 3MA |error| 4MA |error| 1 17 2 21 3 27 4 31 5 19 6 17 7 21 8 Sales for refrigerators are given in the table below. Using a 3-month moving average, forecast sales for February the following year. Calculate the MAD for this model. 3-Month Absolute Month Sales Moving Average Deviation January 11 February 14 March 16 April 10 May 15 June 17 July 11 August 14 September 17 October 12 November 14 December 16 January 11 February Use the weighted moving average to forecast sales for February the following year . Calculate the MAD for this model. Which model is better? Month Sales 3-Month Weighted Moving Average Absolute Deviation January 11 February 14 March 16 April 10 May 15 June 17 July 11 August 14 September 17 October 12 November 14 December 16 January 11 February Lillian Sam, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Sam has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year: Crime Patients Year Rate X Y 1 58.3 36 2 61.1 33 3 73.4 40 4 75.7 41 5 81.1 40 6 89.0 55 7 101.1 60 8 94.8 54 9 103.3 58 10 116.2 61 Column totals 854.0 478 Using trend (linear regression) analysis, predict the number of patients Dr. Sam will see in years 11 and 12 as a function of time. The following gives the number of pints of type B blood used at Woodlawn Hospital in the past 6 weeks: Week of Pints used August 31 360 September 7 389 September 14 410 September 21 381 September 28 368 October 5 374 October 12 Forecast the demand for the week of October 12 using Sales of Volkswagen’s popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). The sales manager had predicted before the new model was introduced that first year sales would be 410 VWs. Using exponential smoothing with a weight of α =.30, develop forecasts for years 2 through 6. Forecast Exponential Absolute Year Sales Smoothing a = 0.6 Deviation 1 450 410.0 2 495 3 518 4 563 5 584 6 Forecast Exponential Absolute Year Sales Smoothing a = 0.9 Deviation 1 450 410.0 2 495 3 518 4 563 5 584 6

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section: Chapter Questions

Problem 33P: Management of a home appliance store would like to understand the growth pattern of the monthly...

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Related questions

Question

Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the

number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table:

Demand for Guitars	3	6	7	5	10	7
Maroon 5 TV Appearances	3	4	7	6	8	5

Graph these data to see whether a linear equation might describe the relationship between the group’s television shows and guitar sales.
Use the least-squares regression method to derive a forecasting equation.
Use the least-squares regression method to derive a forecasting equation.
What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month?

Weekly sales of copy paper at Cubicle Suppliers are provided in the table below. Compute a three-period moving average and a four-period moving average for weeks 5, 6, and 7. Compute the MAD for both forecasting methods. Which model is more accurate? Forecast week 8 with the more accurate method.

Week Sales (cases)

1 17

2 21

3 27

4 31

5 19

6 17

7 21

Answer

Week	Sales (cases)	3MA	\|error\|	4MA	\|error\|
1	17
2	21
3	27
4	31
5	19
6	17
7	21
8

Sales for refrigerators are given in the table below. Using a 3-month moving average, forecast sales for February the following year. Calculate the MAD for this model.

		3-Month	Absolute
Month	Sales	Moving Average	Deviation
January	11
February	14
March	16
April	10
May	15
June	17
July	11
August	14
September	17
October	12
November	14
December	16
January	11
February

Use the weighted moving average to forecast sales for February the following year . Calculate the MAD for this model.

Which model is better?

Month	Sales	3-Month Weighted Moving Average	Absolute Deviation
January	11
February	14
March	16
April	10
May	15
June	17
July	11
August	14
September	17
October	12
November	14
December	16
January	11
February

Lillian Sam, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Sam has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year:

	Crime	Patients
Year	Rate X	Y
1	58.3	36
2	61.1	33
3	73.4	40
4	75.7	41
5	81.1	40
6	89.0	55
7	101.1	60
8	94.8	54
9	103.3	58
10	116.2	61
Column totals		854.0	478

Using trend (linear regression) analysis, predict the number of patients Dr. Sam will see in years 11 and 12 as a function of time.

The following gives the number of pints of type B blood used at Woodlawn Hospital in the past 6 weeks:

Week of	Pints used
August 31	360
September 7	389
September 14	410
September 21	381
September 28	368
October 5	374
October 12

Forecast the demand for the week of October 12 using

Sales of Volkswagen’s popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). The sales manager had predicted before the new model was introduced that first year sales would be 410 VWs. Using exponential smoothing with a weight of α =.30, develop forecasts for years 2 through 6.

		Forecast Exponential	Absolute
Year	Sales	Smoothing a = 0.6	Deviation
1	450	410.0
2	495
3	518
4	563
5	584
6


		Forecast Exponential	Absolute
Year	Sales	Smoothing a = 0.9	Deviation
1	450	410.0
2	495
3	518
4	563
5	584
6

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