Final answer:
The statement is true; the squared correlation (r²) shows the proportion of the variation explained by the model, and 1-r² represents the unexplained variation. An r² of 0.4397 in a given example means 44% of the variation is explained by the model.
Step-by-step explanation:
The statement that the squared correlation (r²) gives the fraction of the data's variation accounted for by the model, and 1-r² is the fraction of the original variation left in the residuals is true. The coefficient of determination, r², is equal to the square of the correlation coefficient, r, and it quantifies how well the regression line predicts the dependent variable. For example, with a correlation coefficient of r = .6631, we have r² = .4397. This means that approximately 44 percent of the variation in final exam grades can be explained by the variation in third exam grades, according to the line of best fit ŵ = -173.51 + 4.83x. Conversely, 1 - r², or approximately 56 percent, represents the variation in final exam grades that isn't explained by the third exam grades using this regression line.