Final answer:
The coefficient of determination, r², is a number that indicates how well data fits the statistical model, representing the percentage of variation in the dependent variable that can be explained by the independent variable using the linear regression model.
Step-by-step explanation:
The coefficient of determination, r², is a number that indicates how well data fits the statistical model. It is equal to the square of the correlation coefficient, 'r', and is usually represented as a percentage. The value of r² can be interpreted as the percentage of variation in the dependent variable that is explained by the variation in the independent variable using the linear regression model. For instance, if the correlation coefficient, r, is 0.6631, then the coefficient of determination would be r² = 0.6631² = 0.4397 or approximately 44 percent. This indicates that approximately 44 percent of the variation in the final exam grades can be explained by the scores on the third exam using the regression line.
The coefficient of determination is a critical statistic in regression analysis, reflecting the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is not the same as the slope of the linear regression, nor is it the error term; instead, it informs us about the effectiveness of our regression model.
Moreover, it is important to consider the sample size and the correlation coefficient, together, to assess the reliability of the linear model.