What is the expected outcome when the coefficient of determination is high in a linear regression model?

When the coefficient of determination, denoted as R², is high in a linear regression model, it indicates that a significant proportion of the variance in the dependent variable can be explained by the independent variable(s). This means that the model is capturing the relationship between the variables effectively, leading to less variability in the predicted outcomes. A high R² suggests that the predictions made by the model are closely aligned with the actual data, reducing the degree to which the outcomes deviate from those predictions.

In practical terms, a high coefficient of determination implies that the model is able to predict the outcome with a degree of accuracy, as it accounts for most of the variability in the dependent variable. This is desirable in a regression analysis as it indicates that the predictors are relevant and useful in explaining the observed data.

Other options, such as increased variability in the dependent variable, indicate a misunderstanding of what a high R² signifies, while claims about the influence of independent variables or the quality of the model fit would also misrepresent the implications of a strong coefficient of determination.