Problem 3-20 (Algo)

An analyst must decide between two different forecasting
techniques for weekly sales of roller blades: a linear trend
equation and the naive approach. The linear trend equation is
F* _{t}* = 124 + 2.1

t |
Units Sold |

11 | 148 |

12 | 149 |

13 | 148 |

14 | 145 |

15 | 153 |

16 | 152 |

17 | 152 |

18 | 159 |

19 | 161 |

20 | 165 |

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**b. **Assuming actual September usage of 64
percent, prepare a forecast for October usage. **(Round
your answer to 2 decimal places.)**

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Answer: Linear Trend Method: Given linear trend equation: y = 124 + 2.1 x t Where t = periods Therefore: Period 11 Forecast = 124 + 2.1 x 11 = 147.10 Period 12 Forecast = 124 + 2.1 x 12 = 149.20 Period 13 Forecast = 124 + 2.1 x 13 = 151.30 Period 14 Forecast = 124 + 2.1 x 14 = 153.40 Period 15 Forecast = 124 + 2.1 x 15 = 155.50 Period 16 Forecast = 124 + 2.1 x 16 = 157.60 Period 17 Forecast = 124 + 2.1 x 17 = 159.70 Period 18 Forecast = 124 + 2.1 x 18 = 161.80 Period 19 Forecast = 124 + 2.1 x 19 = 163.90 Period 20 Forecast = 124 + 2.1 x 20 = 166 Now: Mean Absolute Deviation (MAD)  Formula: MAD =  Absolute Error / n Here: Absolute Error = |Actual - Forecast| Therefore: MAD = (|148 - 147.10| + |149 - 149.20| + |148 - 151.30| + |145 - 153.40| + |153 - 155.50| + |152 - 157.60| + |152 - 159.70| + |159 - 161.80| + |161 - 163.90| + |165 - 166|) / 10 MAD = (0.90 + 0.20 + 3.30 + 8.40 + 2.50 + 5.60 + 7.70 + 2.80 + 2.90 + 1.00) / 10 MAD = 3.53 Mean Squared Error (MSE) MSE =  (Error^2) / (n - 1) Here: Error^2 = (Actual value - Forecast value)^2 Therefore: MSE = ((148 - 147.10)^2 + (149 - 149.20)^2 + (148 - 151.30)^2 + (145 - 153.40)^2 + (153 - 155.50)^2 + (152 - 157.60)^2 + (152 - 159.70)^2 + (159 - 161.80)^2 + (161 - 163.90)^2 + (165 - 166)^2) / (10 - 1) MSE = (0.81 + 0.04 + 10.89 + 70.56 + 6.25 + 31.36 + 59.29 + 7.84 + 8.41 + 1) / (10 - 1) MSE = 21.83 Naive Forecast Method: In the naive forecast approach, the previous period's actual value is used as the current period's forecast, with no formulas or changes. That is: Previous Period Actual = Current Period Forecast Therefore: Period 12 Forecast = 148 Period 13 Forecast = 149 Period 14 Forecast = 148 Period 15 Forecast = 145 Period 16 Forecast = 153 Period 17 Forecast = 152 Period 18 Forecast = 152 Period 19 Forecast = 159 Period 20 Forecast = 161 Now: Mean Absolute Deviation (MAD)  MAD = (|149 - 148| + |148 - 149| + |145 - 148| + |153 - 145| + |152 - 153| + |152 - 152| + |159 - 152| + |161 - 159| + |165 - 161|) / 9 MAD = (1 + 1 + 3 + 8 + 1 + 0 + 7 + 2 + 4) / 9 MAD = 3 Mean Squared Error (MSE) MSE = ((149 - 148)^2 + (148 - 149)^2 + (145 - 148)^2 + (153 - 145)^2 + (152 - 153)^2 + (152 - 152)^2 + (159 - 152)^2 + (161 - 159)^2 + (165 - 161)^2) / (9 - 1) MSE = (1 + 1 + 9 + 64 + 1 + 0 + 49 + 4 + 16) / (9 - 1) MSE = 18.13 Conclusion: The Naive method is most accurate method for this particular data. Reason: The forecasting model is said to be accurate when MAD and MSE values are lowest. The lowest value indicates that the projected data produced less errors when compared to the real data and is also close to the actual data. Please note: The question "b" doesnt have a data associated with it hence cannot be attempted, i request you to attach the corresponding data for the answer. For your reference: ...