Math Problem Statement
A convenience store recently started to carry a new brand of soft drink. Management is interested in estimating future sales volume to determine whether it should continue to carry the new brand or replace it with another brand. The following table provides the number of cans sold per week. Use both the trend projection with regression and the exponential smoothing (let alphaαequals=0.40.4 with an initial forecast for week 1 of 607607) methods to forecast demand for week 1313. Compare these methods by using the mean absolute deviation and mean absolute percent error performance criteria. Does your analysis suggest that sales are trending and if so, by how much?
Period
1
2
3
4
5
6
7
8
9
10
11
12
Sales
607607
628628
644644
743743
652652
624624
725725
719719
740740
740740
671671
759759
Part 2 (i) Obtain the trend projection with regression forecast. The forecast for week 1313 is 756756. (Enter your response rounded to the nearest whole number.) Part 3 Specify the mean absolute deviation (MAD) and mean absolute percent error (MAPE). (Enter your responses rounded to two decimal places.) MAD MAPE 30.6530.65 4.474.47%
Part 4 (ii) Obtain the exponential smoothing forecast. The forecast for week 1313 is enter your response here. (Enter your response rounded to the nearest whole number.)
Solution
To solve this problem, we need to approach it in the following steps:
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Trend Projection with Regression:
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Math Problem Analysis
Mathematical Concepts
Trend Analysis
Regression
Exponential Smoothing
Forecasting
Error Measurement
Formulas
Trend Projection: ŷ = a + bt (linear regression equation)
Exponential Smoothing: Ft+1 = α * Dt + (1 - α) * Ft
MAD (Mean Absolute Deviation): MAD = Σ|Actual - Forecast| / n
MAPE (Mean Absolute Percent Error): MAPE = Σ|(Actual - Forecast)/Actual| * 100 / n
Theorems
Linear Regression Model
Exponential Smoothing Method
Suitable Grade Level
Undergraduate - Business/Statistics
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