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

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

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

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.)

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