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Hi, it's my understanding that the relationship between X and Y changes for different values of X, but I'm not sure if this curved relationship is an objectively good metric.  I would greatly appreciate your help, especially with parts a and c.

Hi, it's my understanding that the relationship between X and Y changes for different values of X, but I'm not sure if this curved relationship is an objectively good metric.  I would greatly appreciate your help, especially with parts a and c.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 11PPS
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Hi, it's my understanding that the relationship between X and Y changes for different values of X, but I'm not sure if this curved relationship is an objectively good metric.  I would greatly appreciate your help, especially with parts a and c.

7. The scatterplot below shows the relationship between two random variables X and Y. Y 9 (O 5 4 3 2 OL 0 OO 1 2 X 00° O oo 3 O (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? (d) 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.)
Transcribed Image Text:7. The scatterplot below shows the relationship between two random variables X and Y. Y 9 (O 5 4 3 2 OL 0 OO 1 2 X 00° O oo 3 O (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? (d) 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.)
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