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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. 12 14 16 23 30 40 50 55 67 72 79 96 112 127 +55 4 10 13 15 15 25 27 45 38 46 53 77 82 99 100 USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows a 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 45. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation a. (Round your answer to two decimal places.) m (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. 12 14 16 23 30 40 50 55 67 72 79 96 112 127 +55 4 10 13 15 15 25 27 45 38 46 53 77 82 99 100 USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows a 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 45. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation a. (Round your answer to two decimal places.) m (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.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 5 12 14 16 23 30 40 50 55 50 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 45 38 46 53 77 82 99 100 USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows a 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 45. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation σ. (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.)
Transcribed Image Text: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 5 12 14 16 23 30 40 50 55 50 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 45 38 46 53 77 82 99 100 USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows a 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 45. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation σ. (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.)
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