Final answer:
A higher r² value for a line of best fit indicates a stronger relationship between the independent and dependent variables, meaning the line can better predict outcomes. The r² value close to 1 represents a stronger model that fits the data more closely, making it more reliable for prediction.
Step-by-step explanation:
A higher percentage for the coefficient of determination, r², for a line of best fit is typically better. A higher r² value, expressed as a percentage, indicates that a greater proportion of the variability in the dependent variable (y) can be explained by the independent variable (x) using the regression line. In the context of an example where we have an original line of best fit with r = 0.6631 and a revised line with r = 0.9121 after removing an outlier, the newer line shows a stronger correlation. This is evident as the r-value is closer to 1, which suggests a better fit to the data values, making it a more predictive and stronger model.
If we consider the square of the original correlation coefficient, r² = (.6631)² = .4397, we can interpret this as 44% of the variability in the final exam grades being explained by the third exam grades. After removing the outlier from the dataset, the line of best fit provided even less deviation from the observed data, indicating a closer fit.