Consider the linear model yᵢ = β₀ + β₁xᵢ₁ + ... + βₚxᵢₚ + eᵢ for i = 1, ... , n where Ee = 0 and Cov(e) = σ²In.

Let x₀ⱼ = ∑ⁿᵢ₌₁xᵢⱼ/n denote the sample mean of the j th explanatory variable for j = 1, ... ,p.

Show that β₀ + β₁x‾1 + ... + βₚx‾ₚ is estimable.