Given that cov(x,y) = 8.5, $$S _ { y } ^ { 2 }$$ = 8 and $$S _ { x } ^ { 2 }$$ = 10, the value of the coefficient of determination is 0.95.

Question

Quizplus · Accepted Answer

The coefficient of determination (r-squared) can be found by squaring the correlation coefficient (r), which is given by the formula:
r = cov(x,y) / (S_x * S_y)
Substituting the given values, we get:
r = 8.5 / (sqrt(10) * sqrt(8)) = 0.873
Therefore, r-squared = 0.873^2 = 0.761 < 0.95. Thus, the given statement is false.

Given That Cov(x,y) = 8 Sy2S _ { y } ^ { 2 }Sy2​

Given That Cov(x,y) = 8 $S _ { y } ^ { 2 }$