For the model y 1 = 1 + x + 1 , y 2 =

For the model
y₁ = α₁ + βx + ε₁,
y₂ = α₂ + ε₂,
y₃ = α₃ + ε₃,

assume that y_i2 + y_i3 = 1 at every observation. Prove that the sample covariance matrix of the least squares residuals from the three equations will be singular, thereby precluding computation of the FGLS estimator. How could you proceed in this case?