What values can the Pearson correlation coefficient (r) take?

Question

Accepted Answer

Values between -1 and 1, inclusive. The Pearson correlation coefficient r ranges from -1 to 1, inclusive. A value of r = 1 indicates a perfect positive linear relationship, r = -1 indicates a perfect negative linear relationship, and r = 0 indicates no linear relationship. Values between these extremes indicate varying degrees of linear association.

Limiting r to positive numbers ignores negative correlations, where one variable increases as the other decreases; many real-world relationships are inversely related. Restricting r to values between 0 and 1 also excludes negative correlations and fails to capture the full range of linear relationships. Allowing any real number is too broad; the correlation coefficient is bounded by -1 and 1 by definition, as it is essentially a standardized measure of co-variation.

The Pearson correlation coefficient is a fundamental concept on the DSST exam. Students should know its range, be able to interpret its magnitude (strength) and sign (direction), understand that it measures only linear relationships (a strong curved relationship might have r ≈ 0), and remember that it is unitless and unaffected by changes of scale.

DSST Principles of Statistics: Question of the Day

Get a free DSST Principles of Statistics question every day

Ready for the full DSST Principles of Statistics? Earn 3 college credits.