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

Mercedes Bailey · Accepted Answer

Final Answer : B, Explanation :  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.

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