HP 3000 Manuals

HP RXForecast Users Manual for MPE Systems

Regression Analysis Formulas 

Variable              Definition                                                                                                     

X                     Matrix of independent variables (N * P) comprised
                      of columns corresponding to intercept, slope, and
                      indicator variables for the seasonality parameters.

Y                     Vector of dependent variables (N).

beta                  Vector of true (unknown) parameters (P).

      ^
     beta             Vector of least squares estimates of beta.

epsilon               Vector of errors (N).

                            ^
     Y = betaX + epsilon  beta = (X'X)-1X'Y

A forecast for (Xh,Yh), where Xh is known is calculated as follows:

     ^           ^
     Yh = X'hbeta

                 ^
           Y'Y-beta'X'Y
     MSE = ------------
                N-P

 A confidence interval for (Xh,Yh) is calculated as follows:

         ^
     S2(Yh) = MSE(X'h(X'X)-1Xh)

     ^            alpha          ^
     Yh +- t(1 - ----- ;N - P)S(Yh)
                    2

 The prediction interval for (Xnew, Ynew) is as follows:

     S2(Ynew) = MSE(1 + X'new(X'X)-1Xnew 

     ^              alpha
     Ynew +- t(1 - ----- ;N - P)S(Ynew)
                      2

MPE/iX 5.0 Documentation