Assume we have a linear model

`Model1`

and`vcov(Model1)`

gives the following matrix:`(Intercept) latitude sea.distance altitude (Intercept) 28.898100 -23.6439000 -34.1523000 0.50790600 latitude -23.643900 19.7032500 28.4602500 -0.42471450 sea.distance -34.152300 28.4602500 42.4714500 -0.62612550 altitude 0.507906 -0.4247145 -0.6261255 0.00928242`

For this example, what does this matrix actually display? What assumptions we can safely make for our model and it’s independent variables?

**Answer**

This matrix displays estimates of the variance and covariance between the regression coefficients. In particular, for your design matrix $\mathbf{X}$, and an estimate of the variance, $\widehat{\sigma}^2$, your displayed matrix is $\widehat{\sigma}^2(\mathbf{X}’\mathbf{X})^{-1}$.

The diagonal entries are the variance of the regression coefficients and the off-diagonals are the covariance between the corresponding regression coefficients.

As far as assumptions go, apply the cov2cor() function to your variance-covariance matrix. This function will convert the given matrix to a correlation matrix. You wil get estimates of the correlations between the regression coefficients. Hint: for this matrix, each of the correlations will have large magnitudes.

To say something about the model in particular, we need point estimates of the regression coefficients to say anything further.

**Attribution***Source : Link , Question Author : forgotten_novel_char , Answer Author : Donnie*