Closing prices of two stocks are recorded for 50 trading days. The sample standard deviation of stock X is 4.638 and the sample standard deviation of stock Y is 9.084. The sample covariance is −36.111. (a) Calculate the sample correlation coefficient.

a) The correlation coeffcient is given by:

And replacing we got:

b) For this case we can conclude that we have a strong, negative linear association between the two stock prices.

Explanation:

Part a

For this case we have the following info:

represent the sample deviation for the variable X

represent the sample deviation for the variable Y

represent the covariance between the variables X and Y

The correlation coeffcient is given by:

And replacing we got:

Part b

Describe the relationship between prices of these two stocks.

For this case we can conclude that we have a strong, negative linear association between the two stock prices.

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