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(d) Calculate 39.5877 ea point estimate of the standard deviation o. (Round your answer to two decimal places.) . ............ 38.13 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 answem four decimal places.) Enter a number. 7:34 t d ENG 10 a (? 21°C A D

(d) Calculate 39.5877 ea point estimate of the standard deviation o. (Round your answer to two decimal places.) . ............ 38.13 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 answem four decimal places.) Enter a number. 7:34 t d ENG 10 a (? 21°C A D

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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# Understanding Linear Regression with Scatter Plots ## Data from a Scatter Plot An article provided a scatter plot with values of \( x \) for rainfall volume (\( \text{m}^3\)) and \( y \) for runoff volume (\( \text{m}^3\)) at a specific location. The accompanying values are: - **x**: 6, 12, 14, 20, 23, 30, 34, 40, 45, 46, 55, 62 - **y**: 4, 10, 13, 15, 25, 27, 30, 34, 40, 46, 60, 89, 104 ## Analysis of Data ### (a) Is there a Linear Relationship? The question asked whether the scatter plot supports using a simple linear regression model. The option selected is: - **No, the scatterplot shows a random scattering with no pattern.** This indicates that the scatter plot does not clearly support a linear relationship. ### (b) Slope and Intercept Estimates The calculated estimates of the population regression line are: - **Slope**: \( 0.8535 \) - **Intercept**: \( -2.2338 \) These estimates describe the line that attempts to best fit the data points in the scatter plot. ### (c) Average Runoff Volume Estimation To estimate the true average runoff volume for a rainfall volume of 49: - **Point Estimate**: \( 39.5877 \, \text{m}^3 \) ### (d) Standard Deviation Estimate To estimate the standard deviation (\( \sigma \)) of the runoff volume: - **Point Estimate**: \( 38.13 \, \text{m}^3 \) ### (e) Variation Proportion The final part asks about the proportion of observed variation in runoff volume attributed to the linear regression relationship between runoff and rainfall. This requires calculation not shown in the document and should be rounded to four decimal places. These analyses provide insights into the relationship between rainfall and runoff using linear regression techniques, although the scatter plot itself did not strongly support a linear model.
Transcribed Image Text:# Understanding Linear Regression with Scatter Plots ## Data from a Scatter Plot An article provided a scatter plot with values of \( x \) for rainfall volume (\( \text{m}^3\)) and \( y \) for runoff volume (\( \text{m}^3\)) at a specific location. The accompanying values are: - **x**: 6, 12, 14, 20, 23, 30, 34, 40, 45, 46, 55, 62 - **y**: 4, 10, 13, 15, 25, 27, 30, 34, 40, 46, 60, 89, 104 ## Analysis of Data ### (a) Is there a Linear Relationship? The question asked whether the scatter plot supports using a simple linear regression model. The option selected is: - **No, the scatterplot shows a random scattering with no pattern.** This indicates that the scatter plot does not clearly support a linear relationship. ### (b) Slope and Intercept Estimates The calculated estimates of the population regression line are: - **Slope**: \( 0.8535 \) - **Intercept**: \( -2.2338 \) These estimates describe the line that attempts to best fit the data points in the scatter plot. ### (c) Average Runoff Volume Estimation To estimate the true average runoff volume for a rainfall volume of 49: - **Point Estimate**: \( 39.5877 \, \text{m}^3 \) ### (d) Standard Deviation Estimate To estimate the standard deviation (\( \sigma \)) of the runoff volume: - **Point Estimate**: \( 38.13 \, \text{m}^3 \) ### (e) Variation Proportion The final part asks about the proportion of observed variation in runoff volume attributed to the linear regression relationship between runoff and rainfall. This requires calculation not shown in the document and should be rounded to four decimal places. These analyses provide insights into the relationship between rainfall and runoff using linear regression techniques, although the scatter plot itself did not strongly support a linear model.
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