Question

If the coefficient of correlation is 0.90, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:
A. 81%
B. 0.81%
C. 90%
D. 0.90%

If the coefficient of determination is 0.975, then the slope of the regression line:
A. could be either positive or negative
B. must be negative
C. must be positive
D. none of the above answers is correct

Answer 1

1. The coefficient of determination gives the percentage of variation.

It is calculated as the square of the correlation coefficient.

0.90^2 = 0.81

Thus, 81% is the answer

2. The sign of the slope of regression and the correlation coefficient is the same. Since, the correlation coefficient is the square root of coefficient of determination.  

And the square root can be either positive or negative.

Option A is correct answer.

ie., The slope could be either positive or negative.