CI for Dependent Variable in Multiple Linear Regression

#1
I have a regression model but I want to get a 95% confidence interval of the dependent variable for given values of the independent variables.

I found that for a single factor regression: Confindence interval = t(alpha, DofF) * SYX * SQRT(1/n+(X-XAVG)^2/SSX)

where n is the number of observations, XAVG is the average of all the independent variables and X is the value for X of the independent variable at the point the CI is wanted.

Is there a way to extend this to multiple linear regression (I have 3 factors)?

Thanks