Range of Values for the Coefficient of Determination

B

R-square ranges from 0-1 inclusive.

The coefficient of determination, denoted as R-squared (R²), is a statistical measure used in regression analysis to determine the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1, inclusive.

The correct answer to the question is B. 0 to +1 inclusive. This means that the coefficient of determination can take any value between 0 and 1, including both 0 and 1.

An R-squared value of 0 indicates that the independent variable(s) have no explanatory power in predicting the dependent variable. In other words, none of the variation in the dependent variable can be attributed to the independent variable(s).

On the other hand, an R-squared value of 1 indicates that the independent variable(s) perfectly explain the variation in the dependent variable. In this case, all the observed data points lie exactly on the regression line, and there is no unexplained variation.

Values between 0 and 1 indicate the proportion of the variance in the dependent variable that can be explained by the independent variable(s). For example, an R-squared value of 0.75 means that 75% of the variation in the dependent variable is accounted for by the independent variable(s), while the remaining 25% is due to other factors or random variation.

It's worth noting that although an R-squared value closer to 1 suggests a better fit of the regression model, it does not necessarily imply the causation or significance of the independent variable(s) in explaining the dependent variable. Other factors such as statistical significance, economic theory, and practical implications should also be considered in interpreting the results of a regression analysis.

In summary, the coefficient of determination (R-squared) ranges between 0 and 1, inclusive, indicating the proportion of the variance in the dependent variable that can be explained by the independent variable(s).