Regression Analysis

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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.

a)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...
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