Assuming a linear relationship between X and Y,if the coefficient of correlation (r)equals −0.75,this means that: A)there is very weak correlation. B)the slope b₁ is = −0.75. C)the value of X is always greater than the value of Y. D)None of these choices are true.

Question

Quizplus · Accepted Answer

The coefficient of correlation (r) measures the strength and direction of the linear relationship between X and Y. A value of −0.75 suggests a fairly strong negative correlation, which means that as X increases, Y tends to decrease.

However, the coefficient of correlation (r) does not necessarily equal the slope (b) of the regression line. The slope represents the amount of change in Y that corresponds to a unit increase in X, while the coefficient of correlation measures only the strength and direction of the linear relationship. Therefore, choice B is not true.

Choice A is also not true because a coefficient of correlation of −0.75 indicates a fairly strong correlation, not a weak one.

Choice C is not necessarily true because the value of X and Y can vary depending on the data and the relationship between them, and the coefficient of correlation alone does not provide information about the magnitude or direction of the difference between X and Y.

Assuming a Linear Relationship Between X and Y,if the Coefficient