Three Variable Regression Model

Y_i = criterion variable for subject i

X1_i = first predictor variable for subject i

X2_i = second predictor variable for subject i

X3_i = third predictor variable for subject i

N = total no. of subjects

Complete Model:

Y_i' = b₀ + b₁X1_i + b₂X2_i + b₃X3_i à SSE(Complete)

A Restricted Model:

Y_i' = b₀ + b₁X1_i à SSE(Restricted)

Null Model: Y_i' = b₀ = M_y à TSS

SSR = SSE(Restricted)-SSE(Complete)

R² = SSR / TSS

df_N = (no. parms complete) - (no. parms restricted) = 2

df_D = N-(no. parms complete) = N-4

MSR = SSR / df_N = SSR/2

MSE = SSE / df_D = SSE/(N-4)

F = MSR/MSE

H0: E[b₂] = E[b₃] = 0

Reject H0 if F statistic computed above exceeds table F at .05 level

or if p < 0.5.