If the coefficient of correlation is –0.81, then the percentage of the variation in y that is explained by the regression line is 81%.

A. True
B. False

True

B. False

Explanation: The coefficient of correlation squared (r²) represents the percentage of variation in y that is explained by the regression line. In this case, (-0.81)² = 0.6561, which means approximately 65.61% of the variation in y is explained by the regression line, not 81%.

B. False

The correct answer is B. False.

The coefficient of correlation, denoted by "r", represents the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

The percentage of the variation in y that is explained by the regression line is represented by the coefficient of determination, denoted by r^2. It ranges from 0 to 1, and it indicates the proportion of the total variation in y that can be explained by the linear relationship with x.

To calculate r^2, you simply square the coefficient of correlation. In this case, since the coefficient of correlation is -0.81, you would calculate (-0.81)^2 = 0.6561.

Therefore, the percentage of the variation in y that is explained by the regression line is 65.61%, not 81%. So the correct answer is B. False.