Consider the linear regression model Y = KB + s, with k independent variables and with \":1 observations {i.e., X is a n x (it: +1) matrix}, as described in the lectures. In the lectures, you learned how to nd a leastsquares {LS} estimator for ,8. The estimator constructed in the lectures is also known as the ordinary L5. This is because there exist other variations of this method. In this exercise. you will construct and investigate one of such variations, known as the weighted L5. The main idea of the weighted L3 is that the observations are not treated as \"equally important". To reect the latter, we consider the weights w1,...,wn, which are strictly positive numbers. Then, the weighted LS estimator ,3 is dened as the value of B that attains the following minirnnm n 127+] 2 l Z lib" (Yr Z; iXa') i=1 _ I _ T _ ggl,gltY X) Wt?\" X), where W := diag[n:1,. . . ,wn} is a square matrix whose diagonal elements are w1,...,wn, and the other ones are zero. Note that X may be random the only assumption we make on X is that it is independent of s