(15 pts) show that the least squares fitted values y^iy^i, for i=1,…,ni=1,…,n, can be written as a linear combination of all observed yjyj values, for j=1,…,nj=1,…,n. that is, show that we can write y^i=∑j=1 hij yj for i=1,…,i^i=∑j=1 hij yj for i=1,…,n. hint: hii=hihii=hi, the leverage of the ithith data point from lecture.

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

Which values of p and q result in an equation with exactly one solution? px-43=-42x+q choose all answers that apply: a) p=-43 and q=-43 b) p=42 and q=43 c) p=43 and q=−42 d) p=42 and q=42

How long must $542 be invested at a rate of 7% to earn $303.52 in interest? in a easier way