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:

  1. 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