Final answer:
The strongest relationship between two variables, given the options, is represented by the correlation coefficient with the highest absolute value. In this case, option D) -.75 indicates the strongest relationship as it has the highest absolute value among the choices.
Step-by-step explanation:
The question at hand requires us to identify which of the provided correlation coefficients represents the strongest relationship between two variables. A correlation coefficient is a statistical measure that describes the size and direction of a relationship between two variables. This coefficient is denoted as r and can range from -1 to +1. The sign of the coefficient indicates the direction of the relationship—positive means the variables move in the same direction and negative means they move in opposite directions. Importantly, whether the coefficient is positive or negative, the absolute value of the coefficient indicates the strength of the relationship—higher absolute values suggest stronger relationships.
Analyzing the options provided: A) .50, B) .25, C) -.25, D) -.75, we can see that option D) -.75 has the largest absolute value and therefore indicates the strongest relationship irrespective of the direction.
To determine the coefficient of determination, which is the square of the correlation coefficient (r^2), one would need a correlation coefficient of approximately 0.71 or -0.71 to achieve a coefficient of determination of at least 0.50, since 0.71^2 = 0.5041, which is just over 0.50.
Therefore, the answer to the student's question is option D) -.75, which represents the strongest relationship between two variables among the provided options.