Which of the following are indications of strong collinearity? (multiple answers)
Best Subset Regression
Large change in the value of a previous coefficient when a new variable is added to the model.
A previously significant variable becomes non-significant when a new independent variable is added
High correlation between two or more independent variables.
Large standard errors and unstable coefficients in the regression model.
The indications of strong collinearity are:
1. Large change in the value of a previous coefficient when a new variable is added to the model.
2. A previously significant variable becomes non-significant when a new independent variable is added.
Therefore, both of these statements are indications of strong collinearity.
To determine indications of strong collinearity, you can examine various factors. Here are some indicators to consider:
1. Best Subset Regression: Strong collinearity can be detected when a best subset regression analysis reveals that adding or removing variables from the model significantly affects the goodness-of-fit statistics or the significance and values of the coefficients. This approach involves systematically considering different combinations of predictor variables to find the best subset that maximizes the model's performance.
2. Large change in the value of a previous coefficient when a new variable is added to the model: When adding a new independent variable to a regression model, if the coefficients of previously included variables undergo significant changes in their values, it suggests a possible presence of collinearity. This change in coefficient values indicates that the model is highly sensitive to the inclusion of additional variables.
3. A previously significant variable becomes non-significant when a new independent variable is added: If a variable that was initially found to be statistically significant (with a low p-value) becomes non-significant (with a high p-value) when another independent variable is added to the model, it implies a potential problem with collinearity. This situation suggests that the new variable might be highly correlated with the previously significant variable, leading to instability in the estimates.
Keep in mind that these indicators are not definitive and collinearity should be confirmed by using appropriate diagnostic methods such as variance inflation factor (VIF) or correlation matrices.