If a significant relationship exists between x and y, what can be inferred about the estimated regression equation if R^2 shows a good fit?

When R-squared (R²) indicates a good fit in the context of a regression analysis, it implies that a significant proportion of the variance in the dependent variable (y) can be explained by the independent variable(s) (x). This strong relationship suggests that the estimated regression equation is effective in capturing the underlying trends and patterns present in the data.

Therefore, the estimation offered by the regression equation is reliable, allowing one to make predictions about the dependent variable based on new observations of the independent variable(s). This predictive power is fundamental in various fields, including business and economics, as it facilitates informed decision-making and strategy development.

While the regression model may have limitations, such as being influenced by the specific dataset in use, the indication of a good fit strengthens the validity of using the equation for estimation and prediction. Thus, this option reflects the practical utility of regression analysis when R² demonstrates a strong correlation.