Final answer:
The answer to the question is D. Correlation coefficient. It measures the strength and direction of the linear relationship between quantitative variables, with its value ranging from -1 to +1.
Step-by-step explanation:
The answer to the student's question is D. Correlation coefficient. The correlation coefficient, often represented by the letter r, quantifies the degree of linear correlation between paired quantitative x- and y-values in a sample. This measurement, known as the Pearson product moment correlation coefficient, tells us both the strength and the direction of the linear association between the independent variable (x) and the dependent variable (y).
The value of r lies between -1 and +1. A positive r indicates that as x increases, y tends to increase and vice versa. Conversely, a negative r suggests that as x increases, y tends to decrease, and inversely. A value of r close to 1 or -1 implies a stronger linear relationship, while a value close to 0 indicates a weaker relationship. The square of the correlation coefficient, r², is referred to as the coefficient of determination, which, when expressed as a percentage, indicates how much variation in the dependent variable can be explained by the independent variable.
One important nuance to understand is that correlation does not imply causation. No matter how strong the correlation, it only signifies a relationship between the changes in variables, not that one variable is causing the change in another. Lastly, when evaluating correlation, the sample size n is also a key factor along with the correlation coefficient r.