The correct answers are
r represents the sample correlation coefficient
p represents the population correlation coefficient
A correlation coefficient of 1 is a perfect positive correlation
A correlation coefficient of -1 is a perfect negative correlation
A correlation coefficient of 0 indicates the variables do not have any direct relationship
Sample Correlation Coefficient (r):
- The sample correlation coefficient (r) is a statistical measure that quantifies the strength and direction of the linear relationship between two variables in a sample of data.
- It ranges between -1 and +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear association, and 0 shows no linear relationship.
- The closer the absolute value of r is to 1, the stronger the linear relationship between the variables.
- The sign of r (+ or -) indicates the direction of the relationship: positive (direct) or negative (inverse).
- The sample correlation coefficient is used to estimate the population correlation coefficient (ρ).
Population Correlation Coefficient (ρ):
- The population correlation coefficient (ρ), also known as the population parameter, represents the true correlation between two variables in the entire population.
- It is a fixed value that remains constant, assuming the population does not change.
- Since we typically don’t have access to the entire population, we estimate ρ using the sample correlation coefficient (r).
- The sample correlation coefficient (r) is considered an unbiased estimator of the population correlation coefficient (ρ) when the sample is representative of the population.