Year Period 1988 1989 1990 1 2 3 Budge ($ billion 3.03 3.29 3.56
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
Transcribed Image Text:### U.S. State General Fund Budget Data (1988-2011)
This table provides the general fund budget for a U.S. state from the year 1988 (Period 1) to 2011 (Period 24). The budgets are listed in billions of dollars.
| Year | Period | Budget ($ billions) |
|------|--------|---------------------|
| 1988 | 1 | 3.03 |
| 1989 | 2 | 3.29 |
| 1990 | 3 | 3.56 |
| 1991 | 4 | 4.41 |
| 1992 | 5 | 4.46 |
| 1993 | 6 | 4.61 |
| 1994 | 7 | 4.75 |
| 1995 | 8 | 5.15 |
| 1996 | 9 | 5.34 |
| 1997 | 10 | 5.66 |
| 1998 | 11 | 6.11 |
| 1999 | 12 | 6.30 |
| 2000 | 13 | 6.58 |
| 2001 | 14 | 6.75 |
| 2002 | 15 | 6.66 |
| 2003 | 16 | 6.88 |
| 2004 | 17 | 7.08 |
| 2005 | 18 | 7.65 |
| 2006 | 19 | 8.48 |
| 2007 | 20 | 8.57 |
| 2008 | 21 | 8.76 |
| 2009 | 22 | 8.53 |
| 2010 | 23 | 8.68 |
| 2011 | 24 | 8.87 |
### Analysis
This dataset indicates a general trend of consistent increase in the state's general fund budget over the 24-year period, with slight fluctuations during certain years. Notable observations include:
- Between 1988 and 1992, there was a steady increase in the budget from $3.03 billion to $4
![### Time Series Analysis
**Example Dataset:**
| Year | Period | Budget ($ billions) |
|-------|--------|---------------------|
| 2010 | 23 | 8.23 |
| 2011 | 24 | 8.86 |
#### (a) Construct a time series plot.
The following diagrams represent different time series plots. Each plot records the budget in billions of dollars against different periods:
1. **First Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- The plot shows an increasing trend in budget values over time until near period 20, where fluctuation and slight decline occur but eventually rise again.
2. **Second Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- The plot shows a strong initial value and then a continuous decreasing trend in budget values over time.
3. **Third Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- Similar to the second plot, showing a strong initial value, followed by a consistent declining trend.
4. **Fourth Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- Similar to the first plot but demonstrating a more stable, consistently rising time series trend.
#### What type of pattern exists in the data?
- **Options:**
1. The time series plot shows a seasonal pattern.
2. The time series plot shows a nonlinear trend.
3. The time series plot shows a horizontal pattern.
4. The time series plot shows a linear trend.
#### (b) Develop a linear trend equation for this time series to forecast the budget (in billions of dollars). (Round your numerical values to three decimal places.)
\[ T_t = \_\_\_\_\_ \]
#### (c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac470ff6-15fd-4fdc-a5f2-c97f7b5a1d30%2F094de28d-3b74-4087-a9d0-0b2646ba89c0%2Fcd3kxqc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Time Series Analysis
**Example Dataset:**
| Year | Period | Budget ($ billions) |
|-------|--------|---------------------|
| 2010 | 23 | 8.23 |
| 2011 | 24 | 8.86 |
#### (a) Construct a time series plot.
The following diagrams represent different time series plots. Each plot records the budget in billions of dollars against different periods:
1. **First Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- The plot shows an increasing trend in budget values over time until near period 20, where fluctuation and slight decline occur but eventually rise again.
2. **Second Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- The plot shows a strong initial value and then a continuous decreasing trend in budget values over time.
3. **Third Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- Similar to the second plot, showing a strong initial value, followed by a consistent declining trend.
4. **Fourth Plot:**
- **X-axis (Horizontal):** Period (ranging from 0 to 25)
- **Y-axis (Vertical):** Budget ($ billions) (ranging from 0 to 10)
- Similar to the first plot but demonstrating a more stable, consistently rising time series trend.
#### What type of pattern exists in the data?
- **Options:**
1. The time series plot shows a seasonal pattern.
2. The time series plot shows a nonlinear trend.
3. The time series plot shows a horizontal pattern.
4. The time series plot shows a linear trend.
#### (b) Develop a linear trend equation for this time series to forecast the budget (in billions of dollars). (Round your numerical values to three decimal places.)
\[ T_t = \_\_\_\_\_ \]
#### (c
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman