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 4 12 14 20 23 30 40 50 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 75 82 99 104 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. 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 X X .84210 intercept -1.86631 (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 45. (Round your answer to four decimal places.) 40.2387 X m 3 (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) 4.78 x 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.) .9801
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 4 12 14 20 23 30 40 50 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 75 82 99 104 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. 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 X X .84210 intercept -1.86631 (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 45. (Round your answer to four decimal places.) 40.2387 X m 3 (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) 4.78 x 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.) .9801
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.CR: Chapter Review Exercises
Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...
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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
4 12 14 20 23 30 40 50 55 67 72 83 96 112 127
y 4 10 13 14 15 25 27 45 38 46 53 75 82 99 104
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.
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
X
X
.84210
intercept -1.86631
(c) Calculate a point estimate of the true average runoff volume when rainfall volume is 45. (Round your
answer to four decimal places.)
40.2387
X m
3
(d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.)
4.78
x 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.)
.9801
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