Which of the following statements about the correlation coefficient r are true?
I. It is not affected by changes in the measurement units of the variables.
II. It is not affected by which variable is called x and which is called y.
III. It is not affected by extreme values.
I only
II and III only
III only
I and II only
I, II, and III
I would say I and II only.
III only
I would say "I and II only" is the best answer. The correlation coefficient, r, is not affected by changes in the measurement units of the variables (statement I) and it is also not affected by which variable is called x and which is called y (statement II). However, it can be affected by extreme values (statement III), so that statement is not true.
I, II, and III
To determine which statements about the correlation coefficient r are true, we can consider each statement individually and explain how to verify its accuracy.
I. "It is not affected by changes in the measurement units of the variables."
This statement is true. The correlation coefficient measures the strength and direction of the linear relationship between two variables, regardless of their measurement units. To confirm this, one can calculate the correlation coefficient for a given set of data using different measurement units and observe that the value of r remains the same.
II. "It is not affected by which variable is called x and which is called y."
This statement is also true. The correlation coefficient measures the association between two variables, regardless of their labels. Swapping the labels of the variables does not affect the value of the correlation coefficient. A simple way to validate this is by calculating the correlation coefficient for a given set of data with different variable labels and observing no change in the value of r.
III. "It is not affected by extreme values."
This statement is not true. Extreme values, also known as outliers, can significantly influence the correlation coefficient. Outliers can exaggerate or diminish the strength of the relationship between two variables, resulting in a different value for the correlation coefficient. To verify this, one can calculate the correlation coefficient with and without extreme values and observe how the value of r changes.
Based on the explanations, the correct answer is "I and II only."