Question

(e) Let Wi denote the random response for the ith observation and denote the associated random error. Suppose the constant variance assumption has been violated such that Var(e) is proportional to (y) = H . That is, Var(€;) = Var(yi) = Chw where c is some constant. Consider a transformed response variable, g(x). We can write the first-order Taylor expansion of g() at Hy, as 9(y) (y) + (y) (yi - My), (1) where g'( ) is the first derivative of g(yi) with respect to y, evaluated at yi = My Using (1), show why a square-root transformation of the response variable such that g(x) = VTi will ensure that the constant variance assumption will approximately hold. That is, show that when a square-root transformation of the response variable is applied, Var[g(y)] = d. (4 marks) where d is a constant.

Answer 1

(R Var lgl Var constaut COnstan t Varye Vart 4 Ayi X X Varlgie) 4

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