The following information regarding a dependent variable y and an independent variable x is provided: ​ The slope of the regression equation is

A) -.667.
B) .667.
C) 100.
D) -100.

The given information is not enough to directly determine the slope of the regression equation. We would need data points and a regression line to calculate the slope. Therefore, we can eliminate choices C and D, as they suggest a fixed value for the slope regardless of the data.

We need to look at choice A and B. Since the slope can be either positive or negative, we cannot eliminate either of the choices based on sign alone. However, one way to determine the correct answer is to note that if y decreases as x increases, the slope must be negative. We can see from the given information that x is increasing while y is decreasing, which indicates a negative relationship. Therefore, the correct answer must be A) -.667, which represents a negative slope.