Final answer:
The correlation coefficient is referred to as being linear because it quantifies the strength and direction of a linear relationship between two variables on a scale of -1 to +1. It is significant when it differs notably from zero, indicating a meaningful linear association.
Step-by-step explanation:
We refer to the correlation coefficient as being linear because it measures the strength and direction of a linear relationship between two variables, typically represented as x and y. The correlation coefficient, denoted by the letter 'r', varies between -1 and +1. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and a value of 0 indicates no linear relationship.
When we say variables are correlated, it means that as one variable changes, the other variable tends to change in a predictable way. If the correlation coefficient is significantly different from zero, it provides evidence of a significant linear relationship between the variables, suggesting that changes in one variable are associated with changes in the other in a linear fashion.
The significance of the correlation coefficient is often tested through a hypothesis test to determine if the observed linear relationship in the sample data can be used to model the relationship in the population.
The coefficient of determination, r², an extension of the correlation coefficient, indicates the proportion of the variance in the dependent variable that is predictable from the independent variable using the regression line.