Homework Help is Here – Start Your Trial Now!
Math
Statistics
The scatterplot below shows the relationship between two random variables X and Y. 9 5 4 3 2 0 8 O 2 X 8 O O 00 3 (a) Is the correlation a good metric for describing the relationship between X and Y for these data? Why or why not? (b) Regardless of your answer to part (a), suppose you calculated the sample correlation between X and Y and found that r = -0.15. Explain in one sentence what this means. (c) If, as noted in (b), r = -0.15 then what is the value of the correlation between 2X and 5 Y?

The scatterplot below shows the relationship between two random variables X and Y. 9 5 4 3 2 0 8 O 2 X 8 O O 00 3 (a) Is the correlation a good metric for describing the relationship between X and Y for these data? Why or why not? (b) Regardless of your answer to part (a), suppose you calculated the sample correlation between X and Y and found that r = -0.15. Explain in one sentence what this means. (c) If, as noted in (b), r = -0.15 then what is the value of the correlation between 2X and 5 Y?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%

The scatterplot below shows the relationship between two random variables X and Y.

 

  • Is the correlation a good metric for describing the relationship between X and Y for these data? Why or why not?

 

  • Regardless of your answer to part (a), suppose you calculated the sample correlation between X and Y and found that r = -0.15. Explain in one sentence what this means.

 

  • If, as noted in (b), r = -0.15 then what is the value of the correlation between 2X and 5Y?

 

  • Based on (b) draw your best approximation to the least squares regression line that fits the data above. Also, make a rough sketch of the corresponding residual plot.  (The sketches do not have to be beautiful but they have to covey the correct information.) 
**Scatterplot Analysis and Correlation** The scatterplot below illustrates the relationship between two random variables \( X \) and \( Y \). ### Scatterplot Explanation - **X-Axis:** The variable \( X \) is represented along the horizontal axis. - **Y-Axis:** The variable \( Y \) is depicted on the vertical axis. - **Data Points:** Individual data points are plotted on the graph, showing the values of \( Y \) corresponding to each \( X \). ### Questions **(a)** Is the correlation a good metric for describing the relationship between \( X \) and \( Y \) for these data? Why or why not? - Consider whether the relationship appears linear or if there are other factors at play that might make correlation an inadequate measure. **(b)** Regardless of your answer to part (a), suppose you calculated the sample correlation between \( X \) and \( Y \) and found \( r = -0.15 \). Explain in one sentence what this means. - A correlation \( r = -0.15 \) indicates a weak negative linear relationship between the variables \( X \) and \( Y \). **(c)** If, as noted in (b), \( r = -0.15 \) then what is the value of the correlation between \( 2X \) and \( 5Y \)? - The correlation remains unchanged when scaling the variables; thus, the correlation between \( 2X \) and \( 5Y \) is also \( -0.15 \).
Transcribed Image Text:**Scatterplot Analysis and Correlation** The scatterplot below illustrates the relationship between two random variables \( X \) and \( Y \). ### Scatterplot Explanation - **X-Axis:** The variable \( X \) is represented along the horizontal axis. - **Y-Axis:** The variable \( Y \) is depicted on the vertical axis. - **Data Points:** Individual data points are plotted on the graph, showing the values of \( Y \) corresponding to each \( X \). ### Questions **(a)** Is the correlation a good metric for describing the relationship between \( X \) and \( Y \) for these data? Why or why not? - Consider whether the relationship appears linear or if there are other factors at play that might make correlation an inadequate measure. **(b)** Regardless of your answer to part (a), suppose you calculated the sample correlation between \( X \) and \( Y \) and found \( r = -0.15 \). Explain in one sentence what this means. - A correlation \( r = -0.15 \) indicates a weak negative linear relationship between the variables \( X \) and \( Y \). **(c)** If, as noted in (b), \( r = -0.15 \) then what is the value of the correlation between \( 2X \) and \( 5Y \)? - The correlation remains unchanged when scaling the variables; thus, the correlation between \( 2X \) and \( 5Y \) is also \( -0.15 \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar 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
SEE MORE TEXTBOOKS