If there is a very weak correlation between two variables, then the coefficient of determination must be
A)much larger than 1, if the correlation is positive
B)much smaller than -1, if the correlation is negative
C)much larger than one
D)None of these alternatives is correct.

Question

Quizplus · Accepted Answer

The coefficient of determination, also known as R-squared, is always between 0 and 1. It represents the proportion of variance in one variable that can be explained by the other variable. Therefore, it cannot be larger than 1 or smaller than 0. Since the question mentions a weak correlation between two variables, it is likely that the coefficient of determination would be closer to 0. None of the given alternatives reflect this understanding, so the correct answer is D.

If There Is a Very Weak Correlation Between Two Variables