If the value of correlation coefficient is positive, then the points in a scatter diagram tend to cluster from lower left corner to upper right corner.

Positive Correlation and Clustered Points in a Scatter Diagram

A scatter diagram is a graphical representation of a set of data points. It is used to determine the relationship between two variables. The correlation coefficient is a statistical measure that quantifies the strength and direction of the relationship between these variables. When the correlation coefficient is positive, it indicates a positive correlation between the variables. In such cases, the points in a scatter diagram tend to cluster in a specific pattern.

Positive Correlation:
When the correlation coefficient is positive, it means that as one variable increases, the other variable also tends to increase. This positive correlation suggests that there is a direct relationship between the variables. For example, if we consider the variables "age" and "income," a positive correlation would imply that as age increases, income also tends to increase.

Points Tend to Cluster:
When the correlation coefficient is positive, the points in a scatter diagram tend to cluster in a specific pattern. This clustering pattern indicates that there is a consistent and predictable relationship between the variables. The closer the points are to each other, the stronger the positive correlation.

Interpretation of Clustered Points:
The clustering of points in a positive correlation indicates that as one variable increases, the other variable also tends to increase. This pattern can be visualized as a trend line that slopes upwards from left to right. The strength of the correlation is determined by how closely the points cluster around this trend line.

Example:
Let's consider the example of a scatter diagram representing the relationship between study hours and test scores. If the correlation coefficient is positive, it suggests that as the number of study hours increases, the test scores also tend to increase. In this scenario, the points in the scatter diagram would cluster around a trend line that slopes upwards.

Conclusion:
When the correlation coefficient is positive, it indicates a positive correlation between the variables. The points in a scatter diagram tend to cluster in a specific pattern, with a consistent and predictable relationship between the variables. The closer the points are to each other, the stronger the positive correlation. Understanding the relationship between variables through scatter diagrams and correlation coefficients helps in making informed decisions and predictions.