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. x 7 12 14 17 23 30 40 47 55 67 72 84 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 71 82 99 104 USE SALT 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 0.8444 intercept -2.3161 X x (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 46. (Round your answer to four decimal places.) 36.5263 x m³ (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationsh 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. x 7 12 14 17 23 30 40 47 55 67 72 84 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 71 82 99 104 USE SALT 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 0.8444 intercept -2.3161 X x (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 46. (Round your answer to four decimal places.) 36.5263 x m³ (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationsh 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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please answer sections d and e
Transcribed Image Text:# Educational Website Transcription: Linear Regression Analysis
## Scatter Plot Data
An article provided a scatter plot with a least squares line for the variables \(x\) (rainfall volume, \(m^3\)) and \(y\) (runoff volume, \(m^3\)) at a specific location. Here are the data points:
- Rainfall Volume (\(x\)): 7, 12, 14, 17, 23, 30, 40, 47, 55, 67, 72, 84, 96, 112, 127
- Runoff Volume (\(y\)): 4, 10, 13, 14, 15, 27, 35, 48, 46, 53, 71, 81, 82, 99, 104
### Use of Simple Linear Regression Model
(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.
### Regression Analysis
(b) **Calculate point estimates of the slope and intercept of the population regression line.**
- Slope: \(0.8444\)
- Intercept: \(-2.3161\)
### Runoff Volume Estimation
(c) **Calculate a point estimate of the true average runoff volume when rainfall volume is \(46\).**
- Estimate: \(36.5263 \, m^3\)
### Standard Deviation
(d) **Calculate a point estimate of the standard deviation \(\sigma\).**
- Standard deviation estimate: \( \) (Answer is not provided in the image, requires calculation.)
### Proportion of Variation
(e) **What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall?**
- Proportion: \( \) (Answer is not provided in the image, requires calculation.)
This analysis allows for the prediction of the runoff volume based on rainfall using a linear regression model. Understanding and estimating these parameters help in creating predictive models for environmental management and resource planning.
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