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The coefficient of determination, denoted as R², quantifies the proportion of variance in the dependent variable that can be explained by the independent variable in a regression model. It ranges from 0 to 1, where 0 indicates no explanatory power and 1 indicates perfect explanation. In this context, R² is calculated as the square of the correlation coefficient (r), providing insight into the strength of the linear relationship between the two variables.

The linear correlation coefficient, represented as r, measures the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where values close to 1 indicate a strong positive correlation, values close to -1 indicate a strong negative correlation, and values around 0 suggest no linear correlation. In the given example, r = 0.298 indicates a weak positive correlation between taxi ride times and tips.

Total variation refers to the overall variability present in a dataset, which can be partitioned into explained variation and unexplained variation. In the context of regression analysis, explained variation is the portion of total variation that is accounted for by the model, while unexplained variation is the portion that remains after fitting the model. Understanding total variation is crucial for interpreting R², as it provides a baseline for assessing how well the model captures the data's variability.