The coefficient of determination $R^2$ represents the proportion of variance in one variable that can be explained by another. In the case of variance inflation factor (VIF), it measures multicollinearity, which is the degree to which one independent variable can be predicted from others.

The formula for calculating the VIF is:

$VIF = \frac{1}{1 - R^2}$

Given that the coefficient of determination $R^2 = 0.50$, we can substitute this value into the formula:

$VIF = \frac{1}{1 - 0.50} = \frac{1}{0.50} = 2$

So, the VIF is 2.

Would you like a further breakdown or more details on how VIF is used in regression analysis?

Here are 5 related questions you might consider:

1. What is the acceptable threshold for VIF values in detecting multicollinearity?
2. How does multicollinearity affect regression models?
3. What methods can be used to reduce multicollinearity?
4. Can VIF be applied in non-linear regression models?
5. How does the interpretation of $R^2$ differ in simple versus multiple regression?

Tip: A VIF value above 10 typically indicates high multicollinearity, which may distort the results of regression analysis.