The problem below looks at forecasting methodologies to determine which forecasting model results in the most accurate forecasts. Accuracy is determined by the lowest mean absolute deviation. Emergency calls to the 911 system of York County for the past 24 weeks are shown below. Accurate forecasts are needed to determine the number of operators needed to staff the station. Week # of Calls 1 50 2 35 3 25 4 40 5 45 6 35 7 20 8 30 9 35 10 20 11 15 12 40 13 55 14 35 15 25 16 55 17 55 18 40 19 35 20 60 21 75 22 50 23 40 24 65 SIMPLE LINEAR REGRESSION Use all of the data, weeks 1 - 24, to calculate the regression equation for this data. Use the weeks (1-24) as the independent variable (x) and number of calls as the dependent variable (y). Once you have the equation, forecast weeks 4 through 24 (enter 4, 5, 6, etc. as the x value in the equation). Calculate the MAD for this forecasting model. Comment on the goodness of fit (R2) and significance of the model (F significance) to determine if this forecast model should be included in the consideration of the different approaches. (If the model is not significant, it cannot be considered, however, you must still make the forecasts and calculate the MAD).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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The problem below looks at forecasting methodologies to determine which forecasting model results in the most accurate forecasts. Accuracy is determined by the lowest mean absolute deviation.

Emergency calls to the 911 system of York County for the past 24 weeks are shown below. Accurate forecasts are needed to determine the number of operators needed to staff the station.

Week	# of Calls
1	50
2	35
3	25
4	40
5	45
6	35
7	20
8	30
9	35
10	20
11	15
12	40
13	55
14	35
15	25
16	55
17	55
18	40
19	35
20	60
21	75
22	50
23	40
24	65

SIMPLE LINEAR REGRESSION

Use all of the data, weeks 1 - 24, to calculate the regression equation for this data. Use the weeks (1-24) as the independent variable (x) and number of calls as the dependent variable (y). Once you have the equation, forecast weeks 4 through 24 (enter 4, 5, 6, etc. as the x value in the equation). Calculate the MAD for this forecasting model. Comment on the goodness of fit (R²) and significance of the model (F significance) to determine if this forecast model should be included in the consideration of the different approaches. (If the model is not significant, it cannot be considered, however, you must still make the forecasts and calculate the MAD).

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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