Assuming a linear relationship between X and Y,if the coefficient of correlation (r)equals -0.30, A) there is no correlation. B) the variance of X is negative. C) variable X is larger than variable Y. D) the slope (b₁) is negative.

Question

Quizplus · Accepted Answer

The coefficient of correlation, r, being positive implies a positive linear relationship between X and Y. As the value of r is 0.30, it indicates a weak positive correlation between X and Y. The slope (b) of the regression line, which measures the change in Y for a unit change in X, is given by b = r * (SD(Y)/SD(X)). Since r is positive, the sign of the slope will be positive if and only if the standard deviation of Y is greater than the standard deviation of X. Therefore, if r = 0.30, it implies that the slope is positive if SD(Y) > 0.30 * SD(X), and negative if SD(Y) < 0.30 * SD(X). Since no information is given about the standard deviations of X and Y, it is not possible to determine the sign of the slope. However, we can conclude with certainty that if the coefficient of correlation is given by r = 0.30, the slope (b) is not negative, and hence the correct choice is option D. The other options are incorrect because none of them can be inferred from the given information.

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