Question

Which statement about correlation is FALSE?

A) Correlation is a quantitative measure of the strength of a linear association between two variables.
B) Correlation is a quantitative measure of the strength of a non-linear association between two variables.
C) A correlation of -1 or 1 corresponds to a perfectly linear relationship.
D) Correlation is measured by r, the correlation coefficient which has a value between -1 and 1.

Answer 1

Correlation is a quantitative measure of the strength of a non-linear association between two variables.

Explanation:

Correlation specifically measures the strength and direction of a linear association between two variables. So we can't use it for all variables or for non-linear associations.

Answer 2

Answer: Choice B

Correlation is a quantitative measure of the strength of a non-linear association between two variables.

Statement B is false because the r value measures the linear association between two variables. In other words, it tells us how good a linear fit we have with a scatterplot of data. So this is why statement A is true.

As r gets closer to +1, then we have a stronger positive linear correlation. If r = 1 exactly, then all points fall on the same straight line with positive slope (the slope isn't necessarily m = 1). Conversely, if r = -1, then the points fall on the same straight line with negative slope (not necessarily m = -1). As r gets closer to r = 0, the strength of the linear relationship weakens. All of this points to statements A, C, and D to be true statements.