3. The Weibull distribution is a type of extreme value distribution that has many applications in engineering; for instance, in hydrology we can use it to model annual minimum flows in river basins. An engineer observes annual minimum flows Z; over a 19-year period in the river Paraguay at Caceres, Brazil, and wishes to estimate a time trend by setting Xi = exp{Bo + Biyear; + Byyear?}. After running the procedure from the previous problem, she obtains a = 11.3 and the following coefficient estimates when regressing Y = Zo on the polynomial basis for year: glm (formula = y - year + I(year 2), family = Gamma(link = "log"), data = caceres) Coefficients: Estimate Std. Error z value Pr(> |z|) (Intercept) 59.534695 0. 767637 77.556