The correlation coefficient r always has the same sign as b₁ in Y = b₀ + b₁X.

Question

Quizplus · Accepted Answer

This is because the correlation coefficient is the ratio of the covariance between X and Y to the product of their standard deviations. Therefore, if b₁ is positive (i.e. X and Y are positively related), then the correlation coefficient will also be positive. Similarly, if b₁ is negative (i.e. X and Y are negatively related), then the correlation coefficient will also be negative.

The Correlation Coefficient R Always Has the Same Sign as B1

The Correlation Coefficient R Always Has the Same Sign as B₁