Final answer:
In a perfect relationship between variables X and Y, the prediction of Y given X is perfect because each value of X has a consistent corresponding value of Y. The correct option is a.
Step-by-step explanation:
When the relationship between X and Y is perfect, the prediction of Y given X is perfect. This is because, in a perfect relationship, every value of the independent variable X is associated with a precise and consistent value of the dependent variable Y.
For instance, if we have a direct linear relationship where Y is directly proportional to X, represented as y = kx where k is the proportionality constant, then for every value of X, there is only one corresponding value of Y, which means the prediction of Y is exactly Y itself, without any error.
Hence, Option a is correct.