**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

See similar textbooks

Related questions

Q: 1. The toco toucan possesses the largest beak relative to body size of all birds. The large surface…

A: In the above given question, it can be observed that the temperatures in degree Celsius in the…

Q: Calculate, for the composite and each of the subject areas, the difference between the national…

A: We see that we have several values corresponding to a given number of subjects. These values are the…

Q: Given the following data for demand at the XYZ Company, calculate the monthly forecast for 2003…

A: Forecast are used to determine the future value over a period of time. Error in forecast can be…

Q: c) Forecast the demand for Week 9 using a three-period simple moving average. The forecasted demand…

A: The number of prints sold each week during the last eight weeks is given.

Q: 5. The values of Alabama building contracts (in millions of dollars) for a 12-month period follow.…

A: The values of Alabama building contracts (in $ millions) for a 12-month period follow. Month…

Q: Compute the one-step-ahead 3-month and 6-month moving-average forecasts for July through December.…

A: Given information: The data presents the sample for the months January through December.

Q: A year later, Barbara gives you a call and tells you that the actual sales for the four quarters of…

A: Given data available in the following tablePeriodForecast valueactual value2017…

Q: Use this data and and generate a model of the annual maintenance expenses based on the age of the…

A: Obtain the regression equation The value of slope is obtained below as follows: From the…

Q: The following data show the average Home Price Index over a six-quarter period. Complete parts a…

Q: Below is data collected over 6 specific years. The data collected is the Consumer Price Index (CPI)…

A: These are the data that have been provided for the dependent and independent variables: Obs. XX…

Q: Find the coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

Q: The table below contains the weekly actual demand and forecasted demand for a product. Week Actual…

A: Given the weekly actual and forecasted demand for the product.Want to calculate MAD, tracking…

Q: a. Build a clearly labeled chart that illustrates the percent of the budget that goes into each…

A: Given a table that shows federal expenditure , we need to use graphical methods to depict the…

Q: Let's examine labor force participation in October 2019, July 2020, and October 2020 Household…

A: Labor Force Participation rate: It is the percentage of the population that is either working or…

Q: If the actual sales for the years 2017, 2018, 2019, and 2020 were 1000, 2000, 3000, and 4000…

A: Years : { 2017,2018,2019,2020 } Actual sales : (X) { 1000,2000,3000,4000 } Forcast for actual…

Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

Q: Does this graph have trends and/or seasonality? What forecasting method is suitable for this data?

A: Introduction: In time series data, trend is the general pattern exhibited by the data over a…

Q: Suppose seafood price and quantity data for the years 2000 and 2009 follow. Use 2000 as the base…

A: Let situation 0 be the Base Period and Situation 1 be the Current Period. Let No be the no. of…

Question

**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) Calculation

In 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 Averages

The 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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Part A

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Time Series Analyses, Forecasting Methods, and Indices$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Below is data collected over 6 specific years. The data collected is the Consumer Price Index (CPI) and the cost of a slice of tuna. We would like to build a model using the CPI to predict the cost of a slice of pizza in a given year. Year 1960 1973 1986 1995 2002 2003 CPI (x) 30.2 48.3 112.3 162.2 191.9 197.8 Cost of a slice of tuna(y) 0.15 0.35 1.00 1.25 1.75 2.00 Plot the data. Are we justified in creating a Linear Regression model to predict the price of a pizza slice using the CPI? Why or why not? Calculate the descriptive statistics. Calculate the sums of squares Calculate the slope, intercept, and correlation. What is this correlation value telling us? Assemble the prediction equation, and interpret the slope within the context of the problem. State the hypotheses for the hypothesis test for regression.
Month Actual demand Forecasted Demand 1 950 1000 2 1070 1000 3 1100 1000 4 960 1000 5 1090 1000 6 1050 1000 For the dataset above, compute the overall MAPE.
Exercise 2. Use the final project data to complete the following questions. Collaborate with your project partners and produce the Excel outputs for the first analysis listed on the project guidelines below. Read and follow the instructions carefully. The Excel outputs such as tables, graphs, summary statistics produced by using Excel. All statistics should not have more than 2 decimal places. All Excel outputs (such as graphs and summary statistics) for each related analysis must be fitted in one sheet. 2. To analyze the total number of items purchased, construct an ungrouped frequency distribution, graph, and find the summary statistics by each type of customer (regular/promotion). Label the graphs completely. Describe the shape of the distribution for each type of customer and discuss similarities or differences by interpreting the graphs and summary statistics. What can you conclude? 3. To analyze customer age, construct a frequency distribution, graph, and find…
Assuming equal effort (# of nets in the water has not changed and the fishing season dates have stayed the same) identify trends in the squid population you see in the data. Based on your textbook reading this week, speculate what processes or dynamics could produce the population trends seen in your data.
Plot the sales revenue figures and appropriate trend line on a graph and identify from this the choice of model for working out the seasonal component. Using the appropriate seasonal model, complete the calculations that are required to produce the required forecasts for quarters 1, 2, 3 and 4 of 2021. On the basis of your analysis explain the recommendation that you would make to ALAW Ltd regarding its future plans.