A study in a university shows that there is relation between

A study in a university shows that there is relation between GRA score and undergraduate GPA of new graduate students. The covariance between GRA score and GPA is 60.74. Also the graduate school records show that GRA variance is 79.21 and variance for GPA is 110.25. What is the correlation coefficient of these two scores 0.65 0.76 0.23 0.86

Solution

Sol)

Correlation coefficient = Covariance/ (standard deviation of x * standard deviation of y)

Now variance of x=79.21 then standard deviation of x= 8.9

variance of y=110.25 then standard deviation of y=10.5

Correlation coefficient = 60.74 / (8.9*10.5) =0.65