Provide an appropriate response.

Question

Which of the following statements concerning the linear correlation coefficient are true?

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.
II: If the slope of the regression line is negative, then the linear correlation coefficient is negative.
III: The value of the linear correlation coefficient always lies between –1 and 1.
IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of –0.82.
(1 point)
a. III and IV
b. I and IV
c. II and III
d. I and II

Answer 1

The correct statements concerning the linear correlation coefficient are:

III: The value of the linear correlation coefficient always lies between –1 and 1.
II: If the slope of the regression line is negative, then the linear correlation coefficient is negative.

I is not necessarily true because a correlation coefficient of zero indicates no linear relationship, but there might still be a non-linear relationship.
IV is false because a correlation coefficient of -0.82 indicates a stronger linear relationship than a correlation coefficient of 0.62, as it is closer to -1.

Given these analyses, the correct option is:

c. II and III