Which of the following are indications of strong collinearity?
Group of answer choices
Best Subset Regression
Large change in the value of a previous coefficient when a new variable is added to the model.
All the Above
A previously significant variable becomes non-significant when a new independent variable is added
All the Above
All of the above are indications of strong collinearity.
The indication of strong collinearity among the given choices is "All the Above". This means that all of the mentioned conditions are indications of strong collinearity in a regression model.
To understand why these conditions indicate collinearity, let's break them down:
1. Best Subset Regression:
Best subset regression is a method used to select the best combination of variables to include in a regression model. If strong collinearity exists among the variables, it becomes challenging to identify the best subset, as the relationships between the variables become highly interdependent.
2. Large change in the value of a previous coefficient when a new variable is added to the model:
When you add a new variable to a regression model with collinearity, it can cause the coefficients of the existing variables to change significantly. This indicates that the existing variables are highly correlated with the new variable, pointing to the presence of collinearity.
3. A previously significant variable becomes non-significant when a new independent variable is added:
Collinearity can lead to inflated standard errors and unstable coefficients. When a new highly correlated variable is introduced, it can 'steal' the explanatory power from the previously significant variable. This results in the previously significant variable becoming non-significant, indicating collinearity.
To identify collinearity more formally, other diagnostics such as variance inflation factor (VIF), correlation matrix, or eigenvalues can also be used. These methods help assess the extent of collinearity and provide more quantitative measures to determine if collinearity is present in the regression model.