bo : -6 by : -4 b₂: -2 4 Year The correct time series plot is plot B ✔ Comment on the appropriateness of a linear trend. A linear trend is not appropriate ✔ Check My Work 5 6 7 b. Develop a quadratic trend equation that can be used to forecast revenue (to 4 decimals). T = b + bit + by Reset Problem 8 9 10 H c. Using the trend equation developed in part (b), forecast revenue in year 11 (to 2 decimals).
bo : -6 by : -4 b₂: -2 4 Year The correct time series plot is plot B ✔ Comment on the appropriateness of a linear trend. A linear trend is not appropriate ✔ Check My Work 5 6 7 b. Develop a quadratic trend equation that can be used to forecast revenue (to 4 decimals). T = b + bit + by Reset Problem 8 9 10 H c. Using the trend equation developed in part (b), forecast revenue in year 11 (to 2 decimals).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
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Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.
Transcribed Image Text:### Linear Regression Analysis in Excel
In this tutorial, you will learn how to conduct a Linear Regression analysis using Excel and the XLMiner Analysis ToolPak. Follow these step-by-step instructions to analyze your data.
#### Data Table
The dataset provided contains the following columns:
- **Year**: Represents the time periods from 1 to 10.
- **Year²**: Square of the year, an optional input for regression involving higher-order terms.
- **Revenue ($ millions)**: Measured revenue in millions of dollars, corresponding to each year.
- **Formula**: Placeholder column currently marked as `#N/A` for any formulas you may introduce.
The data is as follows:
| Year | Year² | Revenue ($ millions) | Formula |
|------|-------|----------------------|---------|
| 1 | | 8.75 | #N/A |
| 2 | | 11.24 | #N/A |
| 3 | | 12.92 | #N/A |
| 4 | | 14.60 | #N/A |
| 5 | | 15.89 | #N/A |
| 6 | | 17.25 | #N/A |
| 7 | | 18.43 | #N/A |
| 8 | | 18.58 | #N/A |
| 9 | | 18.53 | #N/A |
| 10 | | 18.91 | #N/A |
### Part A
**Task**: Use the area below to draw a time series plot.
### Part B
1. **Preparation Step**:
- Open Excel and go to the provided data table.
- Ensure the data is correctly filled in for the columns Year, Year² (optional), and Revenue.
2. **Instructions Area**:
- Read the instructions provided within the shaded area in Excel.
- Delete all the text in the shaded area as instructed.
3. **XLMiner Analysis ToolPak**:
- Use the XLMiner Analysis ToolPak to conduct your Linear Regression analysis. Ensure the tool is installed and active in Excel.
- To use the ToolPak, navigate to the 'Data' tab and select 'Data Analysis'
![### Time Series Analysis and Trend Forecasting
#### Graph Explanation
The graph presented is a time series plot spanning across 10 years (labeled as Year 2 to Year 10 on the x-axis). The y-axis measures an unnamed variable, with values seeming to fluctuate over time. The x-axis intervals are evenly marked in units from 2 up to 10, representing annual data points.
#### Question Analysis
**Part A**:
- **Correct Time Series Plot**:
- Plot B has been identified as the correct time series plot with a checkmark icon indicating confirmation.
- **Comment on the Appropriateness of a Linear Trend**:
- It is noted that "A linear trend is not appropriate" for this data, as confirmed by the accompanying checkmark.
**Part B**:
- **Developing a Quadratic Trend Equation**:
- To forecast the revenue, a quadratic trend equation is proposed, which is of the form:
\[
T_t = b_0 + b_1 t + b_2 t^2
\]
- Missing coefficients (\( b_0, b_1, \text{and } b_2 \)) need to be determined and input into the appropriate fields.
**Part C**:
- **Forecast Revenue for Year 11**:
- Using the quadratic trend equation developed in part (b), the task is to forecast the revenue for Year 11, rounded to two decimal places.
Input fields and buttons:
- **Check My Work**: This button allows users to verify their calculated trend and forecast.
- **Reset Problem**: This button resets the problem to its initial state for reattempt.
By completing these steps, users will gain a deeper understanding of how to apply quadratic trend analysis to time series data and forecast future values based on past trends.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52390996-0048-48b9-99d6-ecc2feddac1b%2Fe137892e-67d1-47a3-8be4-d7b89decf49a%2Fukkrio_processed.png&w=3840&q=75)
Transcribed Image Text:### Time Series Analysis and Trend Forecasting
#### Graph Explanation
The graph presented is a time series plot spanning across 10 years (labeled as Year 2 to Year 10 on the x-axis). The y-axis measures an unnamed variable, with values seeming to fluctuate over time. The x-axis intervals are evenly marked in units from 2 up to 10, representing annual data points.
#### Question Analysis
**Part A**:
- **Correct Time Series Plot**:
- Plot B has been identified as the correct time series plot with a checkmark icon indicating confirmation.
- **Comment on the Appropriateness of a Linear Trend**:
- It is noted that "A linear trend is not appropriate" for this data, as confirmed by the accompanying checkmark.
**Part B**:
- **Developing a Quadratic Trend Equation**:
- To forecast the revenue, a quadratic trend equation is proposed, which is of the form:
\[
T_t = b_0 + b_1 t + b_2 t^2
\]
- Missing coefficients (\( b_0, b_1, \text{and } b_2 \)) need to be determined and input into the appropriate fields.
**Part C**:
- **Forecast Revenue for Year 11**:
- Using the quadratic trend equation developed in part (b), the task is to forecast the revenue for Year 11, rounded to two decimal places.
Input fields and buttons:
- **Check My Work**: This button allows users to verify their calculated trend and forecast.
- **Reset Problem**: This button resets the problem to its initial state for reattempt.
By completing these steps, users will gain a deeper understanding of how to apply quadratic trend analysis to time series data and forecast future values based on past trends.
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