The correct answer is C. Linear: About 87% of the variation of lobster length is associated with its age.
The coefficient of determination, also known as R-squared, represents the proportion of the dependent variable's variance that can be explained by the independent variable(s) in a regression model. A higher R-squared indicates a better fit of the model to the data and suggests that a greater proportion of the variation in the dependent variable (lobster length in this case) can be attributed to the independent variable (age).
In this scenario, the linear model has a coefficient of determination of 0.8724503, indicating that approximately 87% of the variation in lobster length can be explained by age. This suggests a strong relationship between age and length in a linear fashion.
Conversely, the exponential model has a lower coefficient of determination of 0.6730372, indicating that only about 67% of the variation in lobster length is associated with age. While this is still a moderate level of association, the linear model provides a better fit to the data and explains a higher proportion of the variation in length.
Therefore, based on the coefficient of determination, the linear model would be the better choice for projecting the length of a lobster.