Which of the following statements about simple correlation analysis are correct?
A) When all the points in a scatter diagram lie precisely on the estimated regression line, the sample coefficient of correlation will equal 0.
B) When all the points in a scatter diagram lie precisely on the estimated regression line, the sample coefficient of correlation will show the variables to be perfectly correlated.
C) When all the points in a scatter diagram are so widely scattered as to make x completely worthless as a predictor of y, the sample coefficient of correlation will equal 1.
D) All of these.
E) None of these.

Question

Quizplus · Accepted Answer

When all the points in a scatter diagram lie precisely on the estimated regression line, this indicates that the variables are perfectly linearly correlated, and therefore the sample coefficient of correlation will equal 1 or -1 depending on the direction of the correlation. Option A is incorrect because if all the points lie on the regression line, the correlation is perfect and not equal to 0. Option C is incorrect because when the scatter is so widely spread that x is worthless as a predictor of y, the correlation coefficient will be close to 0, not equal to 1. Therefore, the correct option is B.

Which of the Following Statements About Simple Correlation Analysis Are