5. Use quadratic regression to analyze the data in Table 3.4, which relate property taxes and age for a random sample of 19 homes. The response variable Y is property taxes assessed on each home (in dollars), while the explanatory variable X is age of the home (in years). Assume a normal likelihood and the noninformative prior π(β, σ)=1/σ, where

β = (β0, β1, β2) and the model is Yi = β0 + β1Xi + β2X2 i + i. Find the first two moments (hence a point and interval estimate) for the intercept

β0 assuming:

(a) standard frequentist methods.

(b) asymptotic posterior normality (first order approximation).