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 18 23 30 40 49 55 67 72 83 96 112 127 y 4 10 13 15 15 25 27 47 38 46 53 68 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. 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.) m
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 18 23 30 40 49 55 67 72 83 96 112 127 y 4 10 13 15 15 25 27 47 38 46 53 68 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. 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.) m
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...
Related questions
Question
![An article provided a scatter plot and a least squares line with \( x = \) rainfall volume (\( \text{m}^3 \)) and \( y = \) runoff volume (\( \text{m}^3 \)) for a specific location. The following values were taken from the plot:
\[
\begin{array}{c|ccccccccccccc}
x & 4 & 12 & 14 & 18 & 23 & 30 & 40 & 49 & 55 & 67 & 72 & 83 & 96 & 112 & 127 \\
y & 4 & 10 & 13 & 15 & 15 & 25 & 27 & 47 & 38 & 46 & 53 & 68 & 82 & 99 & 104 \\
\end{array}
\]
(a) Does a scatter plot of the data support 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 \( 45 \). (Round your answer to four decimal places.)
\[ [ \text{ } ] \, \text{m}^3 \]
(d) Calculate a point estimate of the standard deviation \(\sigma\). (Round your answer to two decimal places.)
\[ [ \text{ } ] \, \text{m}^3 \]
(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.)
\[ [ \text{ } ] \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc781781c-178e-40a8-bd6a-be56babe6242%2Fa1bfd9df-0d2b-411b-aebb-d8a140e48900%2Ftkf68w4_processed.png&w=3840&q=75)
Transcribed Image Text:An article provided a scatter plot and a least squares line with \( x = \) rainfall volume (\( \text{m}^3 \)) and \( y = \) runoff volume (\( \text{m}^3 \)) for a specific location. The following values were taken from the plot:
\[
\begin{array}{c|ccccccccccccc}
x & 4 & 12 & 14 & 18 & 23 & 30 & 40 & 49 & 55 & 67 & 72 & 83 & 96 & 112 & 127 \\
y & 4 & 10 & 13 & 15 & 15 & 25 & 27 & 47 & 38 & 46 & 53 & 68 & 82 & 99 & 104 \\
\end{array}
\]
(a) Does a scatter plot of the data support 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 \( 45 \). (Round your answer to four decimal places.)
\[ [ \text{ } ] \, \text{m}^3 \]
(d) Calculate a point estimate of the standard deviation \(\sigma\). (Round your answer to two decimal places.)
\[ [ \text{ } ] \, \text{m}^3 \]
(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.)
\[ [ \text{ } ] \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON