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Assignment # 1 Forecasting (Total marks: 100) Following 10 Problems are for submission Problem 1: [12] Registration numbers for an accounting seminar over the past 10 weeks are shown below: |Week 1 2 3 4 5 6 7 8 9 10 | |Registrations 24 23 28 30 38 32 36 40 44 40 | a)Starting with week 2 and ending with week 11, forecast registrations using the naive forecasting method. [2] b)Starting with week 3 and ending with week 11, forecast registration using a two-week moving average. 3] c)Starting with week 5 and ending with week 11, forecast registrations using a four-week moving average. [3] d)Plot the original data and the three forecasts on the same graph. Which forecast smoothes the data the most? Which forecast responds to change the best? [4] Problem 2 [4] Given the following data, use exponential smoothing (( = 0. 3) to develop a demand forecast. Assume the forecast for the initial period is 5. |Period 1 2 3 4 5 6 | |Demand 7 9 5 9 13 8 |
Problem 3 [6] Calculate (a) MAD and (b) MSE for the following forecast versus actual sales figures: |Forecast |104 |112 |125 |132 | |Actual | 95 |108 |128 |136 | Problem 4 [16] Sales of industrial vacuum cleaners at Larry Armstrong Supply Co. over the past 13 months are shown below: |Month |Jan. |Feb. |March |April |May |June |July | |Sales (in thousands) |11 |14 |16 |10 |15 |17 |11 | |Month |Aug. |Sept. |Oct. |Nov. |Dec. |Jan. | |Sales (in thousands) |14 |17 |12 |14 |16 |11 | | a)Using a moving average with 3 periods, determine the demand for vacuum cleaners for next February. [2] b)Using a weighted moving average with 3 periods, determine the demand for vacuum cleaners for February. Use 5, 3, and 2 for the weights of the most recent, second most recent, and third most recent periods, respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would have a weight of 2, and January would have a weight of 3. 4] c)Using MAD, determine which is the better forecast. [5] d)What other factors might Armstrong consider in forecasting sales? [5] Problem 5 [10] 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 | |Demand |17 |19 |15 |21 |20 |23 | Problem 7 [6] A careful analysis of the cost of operating an automobile was conducted by a firm. The following model was developed: Y = 4,000 + 0. 20X where Y is the annual cost and X is the miles driven. )If the car is driven 15,000 miles this year, what is the forecasted cost of operating this automobile? [3] b)If the car is driven 25,000 miles this year, what is the forecasted cost of operating this automobile? [3] Problem 8[12] A study to determine the correlation between bank deposits and consumer price indices in Birmingham, Alabama, revealed the following (which was based on n = 5 years of data): (x = 15, (x2 = 55, (xy = 70, (y = 20 and (y2 = 130 a)What is the equation of the least square regression line? [5] b)Find the coefficient of correlation.
What does it imply to you? [4] c)What is the standard error of the estimate? [3] Problem 9 [8] Given the following data, use least squares regression to develop a relation between the number of rainy summer days and the number of games lost by the Boca Raton Cardinal base ball team. Year1994199519961997199819992000200120022003 Rainy Days15251010302020151025 Games Lost2520101520152010 520 Problem 10 [16] Dr. Jerilyn Ross, a New York City psychologist, specializes in treating patients who are agoraphobic (afraid to leave their homes).
The following table indicates how many patients Dr. Ross has seen each year for the past 10 years. It also indicates what the robbery rate was in New York City during the same year. |Year |1 |2 |3 |4 |5 |6 | |Actual Battery sales |20 |21 |15 |14 |13 |14 | |Forecast |22 | | | | | |
Problem 6: Use the sales data given below to determine: (a) the least squares trend line, and (b) the predicted value for 2000 sales. |Year |1993 |1994 |1995 |1996 |1997 |1998 |1999 | |Sales (units) |100 |110 |122 |130 |139 |152 |164 | To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate year 1993 as year 1, 1994 as year 2, etc. [10] Problem 7
The following data are given. Use least squares regression to derive a trend equation. What is your estimate of the demand in period 7? In period 12? Make comments. [10] |Period |1 |2 |3 |4 |5 |6 | |Demand |7 |9 |5 |11 |10 |13 | Problem 8 As you can see in the following table, demand for heart transplant surgery at a general hospital has increased steadily in the past few years: Year |1 |2 |3 |4 |5 |6 | |Heart transplant |45 |50 |52 |56 |58 |? | The director of medical services predicted 6 years ago that demand in year 1 would be 41 surgeries. a) Use exponential smoothing, first with smoothing constant of 0. 6 and then with one of 0. 9 to develop forecasts for years 2 through 6. [7] b) Use a 3-year moving average to forecast demand in years 4, 5, and 6. 3] c) Use the trend projection method to forecast demand in years 1 through 6. [5] Problem 9 The operations manager of a musical instrument distributor feels that demand for bass drums may be related to the number of television appearances by the popular rock group Green Shades during the previous month. The manager has collected the data shown in the following table: |Demand for bass drum |3 |6 |7 |5 |10 |8 | |Green Shade 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 bass drum sales. [4] b) Use the least squares regression method to derive a forecasting equation. [5] c) What is your estimate for bass drum sales if the Green Shades performed on TV nine times in the last month? [3] Problem 10 The following data relate the sales figure of the bar in a small bed-and breakfast inn to the number of guests registered that week. Week |1 |2 |3 |4 | |Guests |16 |12 |18 |14 | |Bar sales |$300 |270 |380 |300 | a) Perform a linear regression that relates bar sales to guests (not to time). [5] b) If the forecast is for 20 guests next week, what are the sales expected to be? [3]