How do concepts like R-squared, multicollinearity, and statistical tests (T-test vs. F-test) help evaluate linear regression models and interpret their results effectively?

R-squared measures how well the regression model fits the data, indicating the proportion of variance explained. However, it can be inflated by adding more variables, making Adjusted R-squared a better metric for comparing models with different numbers of predictors. Multicollinearity, where predictor variables are highly correlated, can destabilize coefficient estimates and make individual variable interpretations unreliable, though it may not always harm predictive accuracy. Statistical tests like the T-test assess the significance of individual predictor coefficients, while the F-test evaluates the overall significance of the entire model. An unusual scenario where the F-test is not significant but individual T-tests are significant might suggest multicollinearity or other model instabilities.