Could you help on this problem ? Be detailed.

i. (Weighted Least Squares) Consider the simple linear regression model ya: = 150 + E31153; +5: where E{s,-} = U and the errors are independent, but Var(e,;) = 02/10,, where the w,- are known constants, so the errors do not have equal variance. Because the variances are not equal, the standard theory does not apply. Intuitively, it seems that the observations with large variability should inuence the estimates of ,69 and ,61 less than the observations with small variability. The problem can be transformed by multiplying y,- by /wg, so we have a new model Viv-ilk = Vwi + Vwilm + Viv-55 Za: = ui + 451% + 5:; where Z; = myhui = \"173;: \"a = air: and 5i = @512- (a) Show that the new model satises the assumptions of the standard simple linear regression model. (b) Show that the least squares estimates for u and [51 are given by A A A 2 \"with? shy-z - w) o=w-151$'w and 51 = H\". n n 2 maxi 2 my, _ i=1 (1 _1.=1 rw R an y,\" n . Z 11}..- mi The estimates 3.] and Bl are known as the weighted least squares estimates. (c) Show that performing a least squares analysis on the new model is equivalent to minimizing R Z 104%? n 1613:02- i=1 This is a criterion of the weighted least squares method: The observations with large variances are weighted less