Correlation Coefficient

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1.

A correlation coefficient of r = 1 indicates a perfect positive linear relationship between two variables.

A correlation coefficient of r = -1 indicates a perfect negative linear relationship between two variables.

A correlation coefficient of r = 0 indicates no linear relationship between the two variables.

A scatter plot is a graphical representation of two variables, showing how much one variable is affected by another. Each point represents an observation.

A strong positive correlation on a scatter plot appears as points that are closely clustered around a line that slopes upwards from left to right.

A strong negative correlation on a scatter plot appears as points that are closely clustered around a line that slopes downwards from left to right.

Positive correlation means that as one variable increases, the other variable also increases. Negative correlation means that as one variable increases, the other variable decreases.

A weak correlation indicates that there is little to no relationship between the two variables, and the points on a scatter plot are widely dispersed.

The strength of a correlation can be determined by the absolute value of the correlation coefficient (r). Values closer to 1 or -1 indicate stronger correlations.