Question

If a probability plot is such that rXY = 1, what must be true?

a) There's no correlation between X and Y.
b) There's a perfect positive linear relationship between X and Y.
c) There's a perfect negative linear relationship between X and Y.
d) There's a weak correlation between X and Y.

Answer 1

If the correlation coefficient rXY is 1, it means there is a perfect positive linear relationship between X and Y, with all data points lying on a straight line with a positive slope.

Step-by-step explanation:

If a probability plot shows that the correlation coefficient rXY is 1, it indicates a perfect positive linear relationship between the variables X and Y. This means, as X increases, Y also increases proportionally, and this relationship is perfectly linear, meaning all points lie on a straight line with a positive slope.

The correlation coefficient, known as r, always ranges between -1 and +1. A value of +1 signifies a perfect positive correlation, while a value of -1 signifies a perfect negative correlation. If r equals 0, it indicates that there is zero correlation between X and Y, and there is no linear relationship.

Therefore, the correct answer is (b) There's a perfect positive linear relationship between X and Y.