Adjusted R-squared: Adjusted R-squared measures the proportion of variance in the dependent variable that is uniquely explained by the independent variables...
Adjusted R-squared:
Adjusted R-squared measures the proportion of variance in the dependent variable that is uniquely explained by the independent variables in the regression model. It is calculated by subtracting the residual variance from the total variation in the dependent variable and then dividing the result by the total variation.
Model Selection Criteria:
Model selection criteria are used to choose the best model from a set of candidate models by comparing their goodness-of-fit measures. The most commonly used criteria are:
Adjusted R-squared: This measure is a variation of R-squared that takes into account the number of independent variables in the model. A higher adjusted R-squared value indicates a better fit, as it means that a larger proportion of the variation in the dependent variable can be explained by the independent variables.
F-statistic: The F-statistic compares the mean square between groups (independent variables) and the mean square within groups (error term). A high F-statistic indicates that there is a significant difference between the two groups, meaning that the independent variables have a significant impact on the dependent variable.
P-value: The p-value is the probability of obtaining an F-statistic as large as the one that was observed, assuming that the null hypothesis (that the independent variables have no significant effect on the dependent variable) is true. A low p-value (less than 0.05) indicates that the independent variables have a significant impact on the dependent variable, while a high p-value (greater than 0.05) indicates that there is no significant evidence to support the claim that the independent variables have a significant impact on the dependent variable.
Model selection criteria are used to select the model that has the highest adjusted R-squared, the lowest F-statistic, and the lowest p-value