There appears to be a seasonal pattern the data and perhaps a upward linear trend b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Qtr1= 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. Round your answers (in thousands of dollars) to whole number. Revenue + Qtrl + Qtr2 + Qtr3 Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6. Round your answers to whole number. Quarter 1 forecast Quarter 2 forecast $ Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast $ Quarter 4 forecast Quarter 3 forecast Quarter 4 forecast c. Let Period = 1 to refer to the observation in quarter 1 of year 1; Period=2 to refer to the observation in quarter 2 of year 1;... and Period=20 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Round your answers (in thousands of dollars) to whole number. Enter negative value as negative number. The regression equation is: $ $ Revenue= + Qtrl + Qtr2 + Qtr3 + Period Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales for year 6. Round your answers to whole number. $ Xthousands $ Xthousands $ thousands Xthousands Xthousands X thousands Xthousands Xthousands
There appears to be a seasonal pattern the data and perhaps a upward linear trend b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Qtr1= 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. Round your answers (in thousands of dollars) to whole number. Revenue + Qtrl + Qtr2 + Qtr3 Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6. Round your answers to whole number. Quarter 1 forecast Quarter 2 forecast $ Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast $ Quarter 4 forecast Quarter 3 forecast Quarter 4 forecast c. Let Period = 1 to refer to the observation in quarter 1 of year 1; Period=2 to refer to the observation in quarter 2 of year 1;... and Period=20 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Round your answers (in thousands of dollars) to whole number. Enter negative value as negative number. The regression equation is: $ $ Revenue= + Qtrl + Qtr2 + Qtr3 + Period Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales for year 6. Round your answers to whole number. $ Xthousands $ Xthousands $ thousands Xthousands Xthousands X thousands Xthousands Xthousands
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Time Series Analysis and Seasonal Effect Estimation
---
#### Time Series Plot Analysis
**Question:**
What type of pattern exists in the data?
**Answer:**
There appears to be a seasonal pattern in the data and perhaps a(n) `upward linear trend`.
---
#### Developing an Estimated Regression Equation
**Question:**
Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data:
- \( \text{Qtr1} = 1 \) if Quarter 1, 0 otherwise;
- \( \text{Qtr2} = 1 \) if Quarter 2, 0 otherwise;
- \( \text{Qtr3} = 1 \) if Quarter 3, 0 otherwise.
Round your answers (in thousands of dollars) to the whole number.
\[
\text{Revenue} = \underset{ \text{(constant)} }{ \underline{\phantom{000}} } + \underset{ \text{(coefficient)} }{ \underline{\phantom{000}} } \text{Qtr1} + \underset{ \text{(coefficient)} }{ \underline{\phantom{000}} } \text{Qtr2} + \underset{ \text{(coefficient)} }{ \underline{\phantom{000}} } \text{Qtr3}
\]
---
**Question:**
Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6. Round your answers to the whole number.
- **Quarter 1 forecast:** $\underline{\phantom{000}}$ thousands
- **Quarter 2 forecast:** $\underline{\phantom{000}}$ thousands
- **Quarter 3 forecast:** $\underline{\phantom{000}}$ thousands
- **Quarter 4 forecast:** $\underline{\phantom{000}}$ thousands
---
**Question:**
Let \( \text{Period} = 1 \) to refer to the observation in quarter 1 of year 1; \( \text{Period} = 2 \) to refer to the observation in quarter 2 of year 1; ... and \( \text{Period} = 20 \) to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52390996-0048-48b9-99d6-ecc2feddac1b%2F5fb743d5-0dc2-4150-8caf-29b870f6eaee%2Ffafujgf_processed.png&w=3840&q=75)
Transcribed Image Text:### Time Series Analysis and Seasonal Effect Estimation
---
#### Time Series Plot Analysis
**Question:**
What type of pattern exists in the data?
**Answer:**
There appears to be a seasonal pattern in the data and perhaps a(n) `upward linear trend`.
---
#### Developing an Estimated Regression Equation
**Question:**
Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data:
- \( \text{Qtr1} = 1 \) if Quarter 1, 0 otherwise;
- \( \text{Qtr2} = 1 \) if Quarter 2, 0 otherwise;
- \( \text{Qtr3} = 1 \) if Quarter 3, 0 otherwise.
Round your answers (in thousands of dollars) to the whole number.
\[
\text{Revenue} = \underset{ \text{(constant)} }{ \underline{\phantom{000}} } + \underset{ \text{(coefficient)} }{ \underline{\phantom{000}} } \text{Qtr1} + \underset{ \text{(coefficient)} }{ \underline{\phantom{000}} } \text{Qtr2} + \underset{ \text{(coefficient)} }{ \underline{\phantom{000}} } \text{Qtr3}
\]
---
**Question:**
Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6. Round your answers to the whole number.
- **Quarter 1 forecast:** $\underline{\phantom{000}}$ thousands
- **Quarter 2 forecast:** $\underline{\phantom{000}}$ thousands
- **Quarter 3 forecast:** $\underline{\phantom{000}}$ thousands
- **Quarter 4 forecast:** $\underline{\phantom{000}}$ thousands
---
**Question:**
Let \( \text{Period} = 1 \) to refer to the observation in quarter 1 of year 1; \( \text{Period} = 2 \) to refer to the observation in quarter 2 of year 1; ... and \( \text{Period} = 20 \) to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account
Transcribed Image Text:### Exercise 17.32 Algo (Seasonality and Trend)
#### South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $302,000 in the first year of operation to $1,094,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars.
| Quarter | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---------|--------|--------|--------|--------|--------|
| 1 | 17 | 38 | 72 | 97 | 174 |
| 2 | 93 | 135 | 159 | 193 | 290 |
| 3 | 179 | 250 | 332 | 374 | 441 |
| 4 | 13 | 23 | 38 | 80 | 189 |
##### a. Construct a time series plot.
**1. Time Series Plot:**
The graph in the time series plot visualizes the quarterly sales revenue (in thousands of dollars) over five years for South Shore Construction. The x-axis represents the quarters (1 through 20, covering five years), while the y-axis shows the sales values in thousands of dollars, ranging from 0 to 450.
**Plot Details:**
- The plot demonstrates a clear seasonal pattern, with revenue peaking in the third quarter of each year.
- The third quarter consistently shows the highest sales, peaking in Year 5 at $441,000.
- There’s a noticeable upward trend in revenue from Year 1 ($302,000) to Year 5 ($1,094,000).
This graphical representation highlights both the seasonal fluctuations and the overall growth trend of South Shore Construction's sales revenue over the specified period.
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