What does it mean to say two variables are positively associated? Negatively associated?

Verified step by step guidance

1. Understand that association between two variables describes how they change together or relate to each other.
2. When two variables are positively associated, it means that as one variable increases, the other variable tends to increase as well. Similarly, if one decreases, the other tends to decrease.
3. Mathematically, a positive association often corresponds to a positive correlation coefficient, which is greater than 0.
4. When two variables are negatively associated, it means that as one variable increases, the other tends to decrease, and vice versa.
5. A negative association corresponds to a negative correlation coefficient, which is less than 0.

Key Concepts

Positive Association

Positive association between two variables means that as one variable increases, the other variable tends to increase as well. This relationship indicates a direct or proportional connection, often visualized as an upward trend in a scatterplot.

Negative Association

Negative association occurs when one variable increases while the other decreases, showing an inverse relationship. This means the variables move in opposite directions, often represented by a downward trend in a scatterplot.

Correlation

Correlation quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative association) to +1 (perfect positive association), with 0 indicating no linear association.