A threshold model can also motivate the probit model. For it, there is an unobserved continuous response Y* such that the observed y_i = 0 if y_i* ≤ τ and y_i = 1 if y_i* > τ. Suppose that y_i* = µ_i + ε_i, where µ_i = α + βx_i and where {ε_i} are independent from a N(0, σ²) distribution. For identifiability one can set σ = 1 and the threshold τ = 0. Show that the probit model holds and explain why β represents the expected number of standard deviation change in Y* for a 1-unit increase in x.