Final answer:
The coefficient of determination, denoted as r², represents the percentage of variability in the dependent variable explained by an independent variable, indicating how well the data fits a statistical model.
Step-by-step explanation:
The percentage of variability in the dependent variable explained by an independent variable is called the coefficient of determination. This term is represented by r², which is the square of the coefficient of correlation (represented by r). When r is positive, there is a positive association between the variables; when r is negative, there is an inverse association. The correlation coefficient measures the strength of the linear relationship between two variables. The closer the correlation coefficient is to 1 or -1, the stronger the relationship.
To illustrate, consider a scenario where we are looking at the relationship between study time (independent variable x) and test scores (dependent variable y). If the correlation coefficient is r = 0.7, then the coefficient of determination is r² = 0.49 or 49%. This indicates that 49% of the variability in test scores can be explained by the amount of time spent studying.