The correlation coefficient r (-1 ≤ r ≤ 1) is a measure that expresses the relationship between two variables.
r = Sxy / (Sx × Sy)
（Sxy: covariance; Sx and Sy: standard deviations of the respective data）
Interpreting the Correlation Coefficient
- r ≈ 1: strong positive correlation (as one increases, the other also tends to increase)
- r ≈ -1: strong negative correlation
- r ≈ 0: no correlation (or a nonlinear relationship)
Example ①
From a scatter plot, the correlation between “temperature and sales of cold drinks” was r ≈ 0.9. Describe this relationship.
Answer: There is a strong positive correlation. Sales tend to be higher when the temperature is higher.
From a scatter plot, the correlation between “temperature and sales of cold drinks” was r ≈ 0.9. Describe this relationship.
Answer: There is a strong positive correlation. Sales tend to be higher when the temperature is higher.
Key Point
- The correlation coefficient expresses the strength of a linear relationship (-1 ≤ r ≤ 1)
- Even when there is a correlation, a causal relationship does not necessarily exist
Practice Problems
- When r = -0.8, describe the relationship between the two variables.
Answers and Explanations
- Answer: There is a strong negative correlation. As one variable increases, the other tends strongly to decrease.