In the perfect correlation principle, what is the slope?

• A. 0
• B. 1
• C. -1
• D. None

Answer: (B)

When two variables are perfectly correlated, all data points lie exactly on a straight line. If you convert both variables to z-scores (standardize them), the slope of that line equals the correlation coefficient. For a perfect positive relationship, this coefficient is +1, so the standardized slope is 1. In other words, after standardizing, every unit increase in one variable corresponds to exactly one unit increase in the other. This is why the best answer is 1. (Note: in raw units, the slope would be r times the ratio of the standard deviations, but in standardized form it becomes 1 when the correlation is perfect and positive.)