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. Use SALT x 6 12 14 17 23 30 40 48 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 48 38 46 53 70 82 99 103 (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 48. (Round your answer to four decimal places.) m3 (d) Calculate a point estimate of the standard deviation ?. (Round your answer to two decimal places.) m3
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. Use SALT x 6 12 14 17 23 30 40 48 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 48 38 46 53 70 82 99 103 (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 48. (Round your answer to four decimal places.) m3 (d) Calculate a point estimate of the standard deviation ?. (Round your answer to two decimal places.) m3
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
An article gave a
| x | 6 | 12 | 14 | 17 | 23 | 30 | 40 | 48 | 55 | 67 | 72 | 79 | 96 | 112 | 127 |
| y | 4 | 10 | 13 | 15 | 15 | 25 | 27 | 48 | 38 | 46 | 53 | 70 | 82 | 99 | 103 |
(a) Does a scatter plot of the data support the use of the simple linear regression model?
(b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.)
(c) Calculate a point estimate of the true average runoff volume when rainfall volume is 48. (Round your answer to four decimal places.)
m3
(d) Calculate a point estimate of the standard deviation ?. (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.)
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 48. (Round your answer to four decimal places.)
m3
(d) Calculate a point estimate of the standard deviation ?. (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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