Which of the following statements concerning the linear correlation coefficient are true?
1) if the linear correlation coefficient for two variables is zero then there is no relationship between the variables.
2) if the slope of the regression line is negative then the linear correlation coefficient is negative.
3) the value of the linear correlation coefficient always lies between -1 and 1.
4) a linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82.
A) 3 and 4
B) 1 and 4
C) 2 and 3
D) 1 and 2
The correct answer is:
C) 2 and 3
Explanation:
1) This statement is false. If the linear correlation coefficient is zero, it means there is no linear relationship between the variables, but there could still be a nonlinear relationship.
2) This statement is true. The sign of the linear correlation coefficient indicates the direction of the relationship between the variables. A negative slope corresponds to a negative correlation coefficient.
3) This statement is true. The value of the linear correlation coefficient always lies between -1 and 1, inclusive.
4) This statement is false. The magnitude of the linear correlation coefficient indicates the strength of the linear relationship. A value of -0.82 suggests a stronger linear relationship than a value of 0.62, regardless of the sign.