Question

Which of the following are properties of the linear correlation coefficient?

Select all that apply.
A.If r1, then a perfect negative linear relation exists between the two variables.
B.A linear correlation of -0.742 suggests a stronger negative association between two variables than a linear correlation of -0.472.
C.A linear corre tion of 0.639 suggests a stronger linear relation between two variables than a linear correlation of 0.639.
D.The linear correlation coefficient is always between 1 and 1. That is, -15rs1.
E.The correlation coefficient is resistant.
F.If r is close to 0, then little or no evidence of any relation between the explanatory or response variable exists.

Answer 1

The true statements about the linear correlation coefficient are that it ranges from -1 to +1, with values close to these extremes indicating strong relationships, while values close to 0 indicate weak or no linear relationship. The sign indicates the direction of the relationship, and a higher absolute value indicates a stronger association.

Step-by-step explanation:

The linear correlation coefficient, often represented as r, is a statistical measure that reflects the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, where values close to -1 or +1 signify a strong linear relationship, and a value close to 0 indicates a weak or no linear relationship.

The options that correctly describe the properties of the linear correlation coefficient are:

• If r = -1, then a perfect negative linear relation exists between the two variables.
• A linear correlation of -0.742 suggests a stronger negative association between two variables than a linear correlation of -0.472, because its absolute value is closer to 1.
• The linear correlation coefficient is always between -1 and +1, meaning -1 ≤ r ≤ +1.
• If r is close to 0, then there is little or no evidence of any relation between the explanatory or response variable.

It is crucial to note that a high linear correlation does not imply causation between the variables, and correlation coefficients are sensitive to outliers. Also, the correlation coefficient's sign indicates the direction of the relationship, with positive coefficients indicating that the variables tend to move in the same direction and negative coefficients indicating that they move in opposite directions.