Quantitative Methods Formulas

General Multiple Regression Model

= yi = b0 + b1x…. _ bnxn + ei

Mean Square Error (MSE)

= SSE / (n - k - 1)

Mean Square Regression (MSR)

= SSR / k

R²

= RSS / SST

Akaike Information Criteria (AIC)

= n x ln( SSE/n ) + 2(k+1)

Bayesian Information Criteria (BIC)

= n x ln ( SSE/n ) + ln(n) x (k+1)

F Statistic for Nested Models

=[ ( SSE r - SSE u) / q ] / [ SSE u / ( n - k - 1) ] with

( q , n - k - 1) degrees of freedom

Value of Predicted Y

= Y^= b0^ + b1^x1 …. + bkx^k

Simple Linear Trend Model

= y0 = b0 + b1t + et

Log-Linear Trend Model

= ln(yt) = b0 + b1t + et

One Period - Ahead Forecast for AR(1)

= x^(t+1) = b^0 + b^1x(t)

Two Period - Ahead Forecast for AR(2)

= x^(t+2) = b^0 + b^1x^(t+1)

Mean-Reverting Level for an AR(1) Model

= b0 / (1 - b1)

Detecting ARCH

= e²(t) = a0 +a1 e^(t-1) + mhu(t)

Estimated Variance of Errors

= var(t+1) = a^0 + a^1e²(t)