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The residuals for 10 consecutive time periods are given in the following table. 8 Time Period Residual 7 -4 -6 4 1 2 3 +10 +8 +6 +4 6 5 +2 -2 9 -8 10 -10 a. Plot the residuals over time. What conclusion can you reach about the pattern of the residuals over time? b. Based on (a). what conclusion can vou reach about the autocorrelation of the residuals? www

The residuals for 10 consecutive time periods are given in the following table. 8 Time Period Residual 7 -4 -6 4 1 2 3 +10 +8 +6 +4 6 5 +2 -2 9 -8 10 -10 a. Plot the residuals over time. What conclusion can you reach about the pattern of the residuals over time? b. Based on (a). what conclusion can vou reach about the autocorrelation of the residuals? www

MATLAB: An Introduction with Applications
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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### Transcription of Image Content for Educational Purposes #### Residual Analysis Over Time The table below shows residuals for 10 consecutive time periods: | Time Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-------------|----|----|---|---|---|----|----|----|----|-----| | Residual | +10 | +8 | +6 | +4 | +2 | 0 | -2 | -4 | -6 | -10 | **Task:** a. **Plot the residuals over time.** Choose the correct graph from the options provided. b. **Conclusion on Residual Pattern:** Based on the plot, determine the pattern of the residuals over time and the possible autocorrelation. **Graph Options:** 1. **Option A:** - Displays a residual trend starting from approximately +10 at time period 1 and decreasing linearly to approximately -10 by time period 10. 2. **Option B:** - Shows a consistent increase in residuals from -10 to +10, opposite to Option A. 3. **Option C:** - Illustrates a V-shaped pattern, indicating a dip towards the middle time periods. 4. **Option D:** - Displays a downward linear trend similar to Option A, beginning high and ending low. **Conclusion:** - By examining the trends in the graph, we can deduce whether there is an upward, downward, or cyclical pattern in the residuals and discuss the implications of any observed autocorrelation in the data series. These tasks help in understanding the relationship and distribution of residuals, aiding in statistical analyses and model evaluations.
Transcribed Image Text:### Transcription of Image Content for Educational Purposes #### Residual Analysis Over Time The table below shows residuals for 10 consecutive time periods: | Time Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-------------|----|----|---|---|---|----|----|----|----|-----| | Residual | +10 | +8 | +6 | +4 | +2 | 0 | -2 | -4 | -6 | -10 | **Task:** a. **Plot the residuals over time.** Choose the correct graph from the options provided. b. **Conclusion on Residual Pattern:** Based on the plot, determine the pattern of the residuals over time and the possible autocorrelation. **Graph Options:** 1. **Option A:** - Displays a residual trend starting from approximately +10 at time period 1 and decreasing linearly to approximately -10 by time period 10. 2. **Option B:** - Shows a consistent increase in residuals from -10 to +10, opposite to Option A. 3. **Option C:** - Illustrates a V-shaped pattern, indicating a dip towards the middle time periods. 4. **Option D:** - Displays a downward linear trend similar to Option A, beginning high and ending low. **Conclusion:** - By examining the trends in the graph, we can deduce whether there is an upward, downward, or cyclical pattern in the residuals and discuss the implications of any observed autocorrelation in the data series. These tasks help in understanding the relationship and distribution of residuals, aiding in statistical analyses and model evaluations.
### Residual Analysis for Time Series Data The residuals for 10 consecutive time periods are provided in the following table: | Time Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-------------|---|---|---|---|---|---|---|---|---|----| | Residual | +10 | +8 | +6 | +4 | +2 | 0 | -2 | -4 | -6 | -8 | #### Questions: **a. What conclusion can you reach about the pattern of the residuals over time?** - A. A decreasing linear relationship exists. - B. No linear relationship exists. - C. An increasing linear relationship exists. **b. Based on (a), what conclusion can you reach about the autocorrelation of the residuals?** - A. There appears to be a strong positive autocorrelation among the residuals. - B. There appears to be a strong negative autocorrelation among the residuals. - C. There does not appear to be an autocorrelation among the residuals. ### Explanation - **Graph/Diagram Analysis**: - If you plot the provided residual data points on a graph with time periods on the x-axis and residuals on the y-axis, you will observe a clear downward trend, indicating a decreasing linear relationship (Answer to a: A). - This trend suggests a systematic pattern in the residuals, which might imply potential issues such as autocorrelation in a time series context. - **Autocorrelation Conclusion**: - Given the clear pattern, it is likely that there is a strong autocorrelation present (Answer to b: A), specifically a negative autocorrelation, as the values progressively decrease over time.
Transcribed Image Text:### Residual Analysis for Time Series Data The residuals for 10 consecutive time periods are provided in the following table: | Time Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-------------|---|---|---|---|---|---|---|---|---|----| | Residual | +10 | +8 | +6 | +4 | +2 | 0 | -2 | -4 | -6 | -8 | #### Questions: **a. What conclusion can you reach about the pattern of the residuals over time?** - A. A decreasing linear relationship exists. - B. No linear relationship exists. - C. An increasing linear relationship exists. **b. Based on (a), what conclusion can you reach about the autocorrelation of the residuals?** - A. There appears to be a strong positive autocorrelation among the residuals. - B. There appears to be a strong negative autocorrelation among the residuals. - C. There does not appear to be an autocorrelation among the residuals. ### Explanation - **Graph/Diagram Analysis**: - If you plot the provided residual data points on a graph with time periods on the x-axis and residuals on the y-axis, you will observe a clear downward trend, indicating a decreasing linear relationship (Answer to a: A). - This trend suggests a systematic pattern in the residuals, which might imply potential issues such as autocorrelation in a time series context. - **Autocorrelation Conclusion**: - Given the clear pattern, it is likely that there is a strong autocorrelation present (Answer to b: A), specifically a negative autocorrelation, as the values progressively decrease over time.
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