What is the formula for calculating the confidence interval for the expected value of $\hat{y}$ in a multi-variable regression model.
In other words, I'm looking for the following formula just for multi-variable regression: $$ \hat{y_i} \pm t _{1-\frac{\alpha}{2}, n-2} \cdot \sqrt{MSE} \cdot \sqrt{\frac{1}{n}+\frac{{(x_i-\bar{x}})^2}{s_{xx}}} $$