Four objects are weighted two at a time on a spring balance. Denoting the four unknown weights by 81. 82. Ba, 84. The six observations are = Bit Be + CI = Bit Ba + 62 = = By + Ba + 64 = By + BA + 65 = Ba + Ba + 68 where c ~ N(0, o') and iid. (a) Derive by hand: 1 Stat 362/562 - Spring 2021 Assignment 4 Due: July 9th 2021 (i) (4 marks) The least squares estimators of A = (81: 82: 83. 84) in terms of y1. . .. . ys. You may use the R function solve to invert X X. (ii) (2 marks) Find Var(@). (iii) (4 marks) The least-square residuals in terms of y1, ...; $6. (b) Let (. . .., 96) = (4, 12, 9,8,5,6). Compute the following using both R regression functions and the parts above. Include code/output along with discussion. (i) (2 marks) The least squares estimates of 3, and compare with part (a). (ii) (2 marks) The standard errors of P, and compare with part (a). Estimate of. (iii) (2 marks) The least squares residuals, and compare with part (a)