An article gave a scatter plot along with the least squares line of x = rainfall volume (m) and y = runoff volume (m) for a particular location. The accompanying values were read from the plot. x4 12 14 17 23 30 40 46 55 67 72 85 96 112 127 4 10 13 15 15 25 27 44 38 46 53 75 82 99 103 (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 50. (Round your answer to four decimal places.) ]m3

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question
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 17 23 30 40 46 55 67 72 85 96 112 127
y 4 10 13 15
15 25 27 44 38 46 53 75 82
99
103
(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 50. (Round your answer to four decimal places.)
m3
(d) Calculate a point estimate of the standard deviation o. (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 4 12 14 17 23 30 40 46 55 67 72 85 96 112 127 y 4 10 13 15 15 25 27 44 38 46 53 75 82 99 103 (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 50. (Round your answer to four decimal places.) m3 (d) Calculate a point estimate of the standard deviation o. (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.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 1 images

Blurred answer
Knowledge Booster
Correlation, Regression, and Association
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman