Final answer:
The best-fit regression equation is chosen by identifying the model that appropriately reflects the curvilinear relationship in the data and explains the most variance, as indicated by the highest coefficient of determination (r²).
Step-by-step explanation:
The question involves selecting the best-fit regression equation for a set of data. Given the information provided, there is no clear linear relationship between the x and y variables, indicating that a linear regression model is not appropriate. Instead, the curvilinear relationship suggests the need for a non-linear regression model. The choice among the given equations should reflect a curve that fits the data well.
Without specific data points, it is not possible to definitively identify which equation is best. In practice, choosing the best regression equation involves plotting the data, fitting different models, and using statistical measures such as the coefficient of determination (r²) to assess how well each model explains the variance in the data.