11. What are the units of a correlation coefficient and a covariance? Which one is a better measure (covariance or correlation coefficient)? What are the limitations of the covariance?
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Units of a correlation coefficient and a covariance: The correlation coefficient (denoted as r) is a dimensionless quantity, meaning it has no units. It ranges from -1 to 1, indicating the strength and direction of the linear relationship between two Show more…
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Which of the following statements is the most accurate about the correlation coefficient and covariance? The covariance takes values between -1 and 1 while the value of the correlation coefficient can be anything on a real line The value of the correlation coefficient can be used to judge about the strength and the direction of the linear relationship while the value of covariance can be used to describe only the direction of the linear relationship The covariance is generally larger than the correlation coefficient. The covariance and correlation coefficient for the sample are represented by different signs, one is negative while the other is positive and vice versa.
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(a) Compute the covariance between $X$ and $Y$ in Exercise 11 (b) Compute the correlation coefficient $\rho$ for this $X$ and $Y .$
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