# What is the covariance between estimated coefficient of a regression model?

Consider the simple linear regression model:
\begin{align} Y_i &= \beta_1 + \beta_2X_i + u_i \\ \hat{Y}_i &= b_1 + b_2X_i \end{align} (a) Show that the regression line always passes through the point $(\bar X, \bar Y)$. What does this imply about the covariance between $b_1$ and $b_2$?

I have been reading a lot about covariance matrix, but how does it relate to X bar and Y bar? The only time when cov appears is in b2 = cov(x,y) / var (x,y) The regression that passes through X bar Y bar can be shown via RSS.

• Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. – gung Jan 23 '18 at 13:16
• The only time when cov appears is in b2 = cov(x,y) / var (x,y) The regression that passes through Xbar Ybar can be shown via RSS – John Jan 24 '18 at 6:22
• Please explain terms in two models and covariance between b1 and b2 ? – Subhash C. Davar Jan 26 '18 at 1:53