Answered: Given the following data, use…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Given the following data, use exponential smoothing with α=0.1 and α=0.6 to generate forecasts for periods 2 through 6. Use Mad and MEE to decide which of the two models produce a netter forecast. (Assume the forecast for Period 1 is 17)

Period	Actual	Forecast
1	14	17
2	16
3	16
4	11
5	12
6	17

a.What is the forecast for Period 6 when you use α=0.6? (Express it to 2 decimal places)

Answer:

b.What is the value of Mean Absolute Deviation (MAD) when α=0.6? Calculate to 3 decimal places. (Use all forecasted values from Period 1 to Period 6.)

Answer:

c.Which method produces a better forecast? (Use all forecasted values from Period 1 to Period 6.)

Select one:

α=0.1 produces a better forecast measured both by MAD and MSE.
When we use MAD, α=0.1 produces a better forecast.
When we use MSE, α=0.1 produces a better forecast.
α=0.6 produces a better forecast measured both by MAD and MSE.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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