Calculating R Gives One Positive and One Negative Example

What is r in statistics?

The correlation coefficient r (Pearson's r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1:

• +1 indicates a perfect positive linear relationship
• 0 indicates no linear relationship
• -1 indicates a perfect negative linear relationship

Values between 0 and 1 (or 0 and -1) indicate weaker relationships. The absolute value of r shows the strength of the relationship, while the sign shows the direction.

Positive and negative examples of r

Positive correlation example (r ≈ +0.8)

Suppose you measure the hours students study (X) and their exam scores (Y). If students who study more tend to get higher scores, you'd see a positive correlation. A value like r = +0.8 would indicate a strong positive relationship.

Negative correlation example (r ≈ -0.7)

Consider the relationship between the number of hours a person exercises (X) and their body fat percentage (Y). If people who exercise more tend to have lower body fat, you'd see a negative correlation. A value like r = -0.7 would indicate a strong negative relationship.

How to calculate r

The formula for Pearson's r is:

This formula calculates the covariance between X and Y divided by the product of their standard deviations. The result is always between -1 and +1.

Interpreting the results

When you calculate r, consider these guidelines:

• If r is positive, as one variable increases, the other tends to increase
• If r is negative, as one variable increases, the other tends to decrease
• The closer r is to 0, the weaker the relationship
• The closer r is to ±1, the stronger the relationship

Remember that correlation does not imply causation. Just because two variables are correlated doesn't mean one causes the other.