**Problem 15-07**Refer to the gasoline sales time series data in the given table.**GASOLINE SALES TIME SERIES**| Week | Sales (1000s of gallons) ||------|--------------------------|| 1 | 17 || 2 | 21 || 3 | 19 || 4 | 23 || 5 | 18 || 6 | 16 || 7 | 20 || 8 | 22 || 9 | 22 || 10 | 21 || 11 | 15 || 12 | 22 |This table represents the time series data for gasoline sales measured in thousands of gallons over a period of 12 weeks. Each row corresponds to a specific week and the corresponding sales volume in thousands of gallons. The data can be used to analyze trends, seasonality, or other patterns in gasoline sales over the given weeks. ### Moving Averages and Mean Squared Error (MSE) CalculationIn this exercise, we will compute the four-week and five-week moving averages for a time series of sales data. We will round our answers to two decimal places. Additionally, we will compute the Mean Squared Error (MSE) for both the four-week and five-week moving averages based on the provided data.#### a. Four-Week and Five-Week Moving AveragesThe table below displays the weekly sales data along with blank columns where we will calculate the moving averages.| Week | Sales | 4-Week Moving Average | 5-Week Moving Average ||------|-------|------------------------|------------------------|| 1 | 17 | | || 2 | 21 | | || 3 | 19 | | || 4 | 23 | | || 5 | 18 | | || 6 | 16 | | || 7 | 20 | | || 8 | 22 | | || 9 | 15 | | || 10 | 20 | | || 11 | 15 | | || 12 | 22 | | |To compute the moving averages for weeks 5 to 12, follow these steps:**Four-Week Moving Average**- Calculate the average of the previous 4 weeks sales for each week starting from week 5.- For example, the four-week moving average for week 5 = (Sales for week 1 + Sales for week 2 + Sales for week 3 + Sales for week 4) / 4.**Five-Week Moving Average**- Calculate the average of the previous 5 weeks sales for each week starting from week 6.- For example, the five-week moving average for week 6 = (Sales for week 1 + Sales for week 2 + Sales for week 3 + Sales for week 4 + Sales for week 5) / 5.#### b. Mean Squared Error (MSE)The Mean Squared Error (MSE) is a measure of the quality of an estimator—it is always non-negative, and values closer to

The formula for moving average is: The formula for mean square error is:

4-Week 5-Week Week Sales Moving Average Moving Average 1 17 21 3 19 4 23 5 18 6. 16 20 8 18 9 22 10 20 11 15 12 22 b. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations to four decimal places and round your final answers to two decimal MSE for four-week moving average = MSE for five-week moving average =

4-Week 5-Week Week Sales Moving Average Moving Average 1 17 21 3 19 4 23 5 18 6. 16 20 8 18 9 22 10 20 11 15 12 22 b. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations to four decimal places and round your final answers to two decimal MSE for four-week moving average = MSE for five-week moving average =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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