The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representativ data. 50 71 55 50 33 58 79 26 y| 161 1938 57 31 11 14 44 16 69 44 37 70 20 45 49 y 278 47 180 22 52 194 34 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) y = -296.881 + 9.963x Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density 401 corresponding residual -379 Predict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density 411 corresponding residual 1528 How do the residuals compare? O The residual for the first point is positive, while the residual for the second point is negative. O The residuals for both points are negative. O The residual for the first point is negative, while the residual for the second point is positive. O The residuals for both points are positive. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.)
The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representativ data. 50 71 55 50 33 58 79 26 y| 161 1938 57 31 11 14 44 16 69 44 37 70 20 45 49 y 278 47 180 22 52 194 34 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) y = -296.881 + 9.963x Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density 401 corresponding residual -379 Predict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density 411 corresponding residual 1528 How do the residuals compare? O The residual for the first point is positive, while the residual for the second point is negative. O The residuals for both points are negative. O The residual for the first point is negative, while the residual for the second point is positive. O The residuals for both points are positive. (b) Calculate the coefficient of determination. (Round your answer to three decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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
Transcribed Image Text:The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior.
One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative
data.
50
71
55
50
33
58
79
26
161
1938
57
31
11
14
44
16
69
44
37
70 20
45
49
278 47
180
22
52
194 34
(a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.)
y = -296.881+ 9.963x
Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.)
colony density
401
corresponding residual
|-379
Predict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.)
colony density
411
corresponding residual
1528
How do the residuals compare?
The residual for the first point is positive, while the residual for the second point is negative.
The residuals for both points are negative.
The residual for the first point is negative, while the residual for the second point is positive.
O The residuals for both points are positive.
(b) Calculate the coefficient of determination. (Round your answer to three decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
Knowledge Booster
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.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman