# Correlation influence on two variable coefficients

Consider the linear model $Y = B_{0} + B_{1}X_{1} + B_{2}X_{2} + e$, where the columns $X_{1}$ and $X_{2}$ of the design matrix have mean $0$ and length $1$. That is $X_{i}'X_{i} = 1$ and $X_{i}'J = 0$ where $J$ is a column entirely of ones. Let $\rho$ be the correlation between $X_{1}$ and $X_{2}$.

Q: Determine what values of $\rho$ will make the variance of $\hat{B}_1$ and $\hat{B}_2$ larger than $5\sigma^2$.

A: My thought is that this is a question related to the variance inflation factor. Therefore, I could plug in $1 / (1 - z^2) = 5$. Here, $z$ is the correlation I am trying to solve for. After performing a few algebra steps, I get $z = 0.8$ (Correlation). Please let me know if I am on the right track with the variance inflation factor or if I am supposed to use another methodology (covariance matrix, etc.) Thank you.