It's not really clear what you're asking from all the notation. I assume by MSE, you're referring to mean square error? MSE is a very general term... but the title of your question is multiple linear regression. So are you referring to a regression concept (like the standard error of the estimate?) S(y0) could refer to the standard deviation of y or predicted y, and S(y0)*S(y0) the variance, but it's unclear from what you're asking.

Could you clarify your notation? And perhaps state the purpose behind this question? That will help in answering it. In what context do you need an answer? Is this being used in a web app somehow?

Could you clarify your notation? And perhaps state the purpose behind this question? That will help in answering it. In what context do you need an answer? Is this being used in a web app somehow?