Final answer:
The correlation coefficient (r) indicates the direction and strength of a linear relationship between two variables. A positive r represents a direct relationship, a negative r an inverse relationship, and the closer the value is to -1 or 1, the stronger the relationship.
Step-by-step explanation:
The correlation coefficient r is a statistical measure that calculates the strength and direction of a linear relationship between two variables on a scatterplot. The value of r ranges from -1 to 1, where:
- A positive correlation coefficient (0 < r < 1) indicates that as one variable increases, so does the other and vice versa, suggesting that the variables move in the same direction.
- A negative correlation coefficient (-1 < r < 0) indicates that as one variable increases, the other decreases, and the opposite is also true, meaning the variables move in opposite directions.
- If there is no correlation (r = 0), this means that there is no linear relationship between the variables.
The strength of the relationship is determined by how close the value of r is to -1 or 1. The closer it is to these extremes, the stronger the correlation. The weakest relationship is when r is closest to 0, which means the variables have little or no linear correlation. Therefore, a correlation coefficient of -0.90 indicates a stronger relationship than a correlation coefficient of -0.50 because it is closer to -1.