A genetic association study considers a large number of explanatory variables, with nearly all expected to have no effect or a very minor effect on the response. An alternative to the least squares estimator ????̂ for the linear model incorporating those explanatory variables is the null model and its estimator,

????̃ = 0 except for the intercept. Is ????̃ unbiased? How does var(????̃

j) compare to var(????̂

j)? Explain why ∑

j E(????̃

j − ????j)

2 < ∑

j E(????̂

j − ????j

)

2 unless n is extremely large.