Like the ratio estimator, a regression estimator can also be used to improve the precision of the estimate. Ratio estimation works well if data are well fit by a straight line through the origin (Lohr). However, this may not always be the case. Data may appear to have a linear fit that may not pass through the origin. In this case, y=B0+B1x would provide a better fit. Given a sample size n, the regression coefficient and intercept can be estimated as B^1=iS(xix)2iS(xix)(yiy)andB^0=yB^1xY can be estimated when X is known using the regression line such that y^=B^0+B^1X. Prove the following: a. E(y^Y)=Cov(B^1,x) b. MSE(y^)(1f)nSy2(1R2), where R=(N1)SxSyi=1N(xiX)(yiY).