An article gave a scatter plot along with the least squares line of x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. The accompanying values were read from the plot. 6 12 14 19 23 30 40 49 55 67 72 81 96 112 127 y 4 10 13 15 15 25 27 48 38 46 53 71 82 99 103 USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows reasonable linear relationship. O Yes, the scatterplot shows a random scattering with no pattern. O No, the scatterplot shows a reasonable linear relationship. O No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 47. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) m³ (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)
An article gave a scatter plot along with the least squares line of x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. The accompanying values were read from the plot. 6 12 14 19 23 30 40 49 55 67 72 81 96 112 127 y 4 10 13 15 15 25 27 48 38 46 53 71 82 99 103 USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows reasonable linear relationship. O Yes, the scatterplot shows a random scattering with no pattern. O No, the scatterplot shows a reasonable linear relationship. O No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 47. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) m³ (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)
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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Transcribed Image Text:### Educational Resource: Linear Regression Analysis
#### Introduction
An article provided a scatter plot along with the least squares line of \( x = \) rainfall volume (\( \text{m}^3 \)) and \( y = \) runoff volume (\( \text{m}^3 \)) for a specific location. The following values were read from the plot:
| \( x \) | 6 | 12 | 14 | 19 | 23 | 30 | 40 | 49 | 55 | 57 | 72 | 81 | 96 | 112 | 127 |
| -------|---|----|----|----|----|----|----|----|----|----|----|----|----|----|-----|
| \( y \) | 4 | 10 | 13 | 15 | 15 | 27 | 28 | 48 | 46 | 53 | 71 | 82 | 99 | 103 | 93 |
#### Graphs and Diagrams
The scatter plot is not visually provided, but it is implied to demonstrate the relationship between rainfall volume and runoff volume.
### Questions and Solutions
**(a) Does a scatter plot of the data support the use of the simple linear regression model?**
- ☐ Yes, the scatterplot shows a reasonable linear relationship.
- ☐ Yes, the scatterplot shows a random scattering with no pattern.
- ☐ No, the scatterplot shows a reasonable linear relationship.
- ☐ No, the scatterplot shows a random scattering with no pattern.
**(b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.)**
- Slope: _______________
- Intercept: _______________
**(c) Calculate a point estimate of the true average runoff volume when rainfall volume is \( 47 \). (Round your answer to four decimal places.)**
- _______________ \( \text{m}^3 \)
**(d) Calculate a point estimate of the standard deviation \( \sigma \). (Round your answer to two decimal places.)**
- _______________ \( \text{m}^3 \)
**(e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)**
- _______________
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