Question

Which of the following statements about correlation are true?

1) The correlation coefficient (r) has no units of measurement.
2) Correlation can never be equal to zero.
3) A negative correlation is always weaker than a positive correlation.
4) Correlation makes no distinction between explanatory and response variables.
5) Correlation can be greater than 1.
6) The correlation coefficient (r) does not change when we change units.

Answer 1

True statements about correlation include that the correlation coefficient has no units, makes no distinction between variables, and is unaffected by changes in units. Correlation can be positive, negative, or zero and the sign does not determine the strength.

Step-by-step explanation:

Of the statements about correlation provided, the following are true:

• The correlation coefficient (r) has no units of measurement.
• Correlation makes no distinction between explanatory and response variables.
• The correlation coefficient (r) does not change when we change units.

This is because the correlation coefficient is a dimensionless measure that indicates the strength and direction of a linear relationship, where 'r' can range from -1 to +1. An r value of 0 indicates zero correlation, meaning there is no linear relationship between the variables. Contrary to the provided statements, correlation can be equal to zero and is not always positive or negative; it depends on the direction of the relationship between the variables. Moreover, a negative correlation is not inherently weaker than a positive one; strength is indicated by how close the value of 'r' is to 1 or -1, not the sign.