Find the coefficient of correlation of the line that best fits the data set. $\{ ( 3,3 ) , ( 5,4 ) , ( 7,6 ) \}$
A) $r = 0.9820$
B) $r = - 0.9820$
C) $r = - 0.7856$
D) $r = 0.3641$
E) $r = 0.7856$

Question

Find the coefficient of correlation of the line that best fits the data set.   $\{ ( 3,3 ) , ( 5,4 ) , ( 7,6 ) \}$  
A) $r = 0.9820$
B)  $r = - 0.9820$
C)  $r = - 0.7856$
D)  $r = 0.3641$
E)  $r = 0.7856$

Quizplus · Accepted Answer

The coefficient of correlation, $r$, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 means a perfect positive linear relationship, -1 means a perfect negative linear relationship, and 0 means no linear relationship. To find $r$ for a small dataset, we can use the formula for Pearson's correlation coefficient. Given the small size of the dataset, we can manually calculate or use statistical software to find $r$. The calculation involves finding the means of the x-values and y-values, the standard deviations of x and y, and the covariance of x and y. Plugging these values into the formula for $r$, we find that the coefficient of correlation that best fits the given data set is $r = 0.9820$, indicating a very strong positive linear relationship between the x and y variables in the dataset.

Find the Coefficient of Correlation of the Line That Best {(3,3),(5,4),(7,6)}\{ ( 3,3 ) , ( 5,4 ) , ( 7,6 ) \}{(3,3),(5,4),(7,6)}

Find the Coefficient of Correlation of the Line That Best $\{ ( 3,3 ) , ( 5,4 ) , ( 7,6 ) \}$