Asked by Scarlet Deven on Sep 24, 2024
Verified
If the coefficient of correlation r = −.81,the standard deviations of x and y are 20 and 25,respectively,then cov(x,y)must be −405.0.
Standard Deviations
An assessment measure that determines the degree of deviation or scattering of data points around the average.
Correlation R
A statistical measure known as Pearson's correlation coefficient that quantifies the degree and direction of linear relationship between two variables.
Cov(x,y)
The covariance between two variables X and Y, measuring how changes in one variable are associated with changes in a second variable.
- Calculate the coefficient of correlation from given data and understand its significance.
- Analyze the relationship between covariance, the coefficient of correlation (r), and the strength and direction of linear relationships.
Verified Answer
cov(x,y) = r * (std dev of x) * (std dev of y)
Substituting the given values:
cov(x,y) = (-0.81) * 20 * 25
cov(x,y) = -405
Therefore, the statement is true and the answer is A.
Learning Objectives
- Calculate the coefficient of correlation from given data and understand its significance.
- Analyze the relationship between covariance, the coefficient of correlation (r), and the strength and direction of linear relationships.
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