Final answer:
The correlation coefficient, r, measures the strength and direction of a linear relationship between two variables, with values ranging from -1 to +1. A positive or negative r indicates a positive or negative linear correlation, respectively, but does not imply causation.
Step-by-step explanation:
The correlation coefficient, denoted as r, is a statistical measure that calculates the strength and direction of a linear relationship between an independent variable x and a dependent variable y. Understanding the value and significance of r in the context of data correlation can be challenging.
It ranges between -1 and +1, where values close to the extremes indicate a stronger linear relationship, and a value of 0 indicates no linear correlation. If r is positive, there is a positive correlation, meaning as x increases, y increases, and as x decreases, y decreases.
Conversely, a negative r value indicates a negative correlation, in which as x increases, y decreases, and vice versa.
Moreover, r alone does not imply causation between the variables. The sign of r is consistent with the slope of the best-fit line in a scatter plot. r must be interpreted along with the sample size and the coefficient of determination, r², to assess the reliability and predictive quality of the linear model.
If r is significant and the scatter plot shows a linear trend within the domain of observed x values, the linear model can be used for prediction.