Suppose that an experimenter postulates a model of the type, Y = + x + , i = 1, 2, , n,

Suppose that an experimenter postulates a model of the type, Y = β + β x + ϵ , i = 1, 2, …, n, when, in fact, an additional variable (say, x independent of x ) also contributes linearly to the response. The true model is then given by: Y = β + β x +

β x + ϵ , i = 1, 2, …, n. Establish that the estimator i 0 1 1i i 2 1 i 0 1 1i 2 2i i is an unbiased estimator for β .