The useful theoretical model Y,- = ,8 X; + D', where Di represents the deviation from the line, can be used to compare various quotient estimators. For a given value of X = x, suppose that the values of Y are scattered around the line, so that the expectation and variance of the deviations are: E[D||X = I] = 0andV[D||X = I] = 021"\")- Consider a. general estimator of ,3 having the form b = 22:0 egyi, Where c.- niay depend on x.,-. a) Find a condition on the coefcients to ensure that b is an unbiased estimator of 5, given the x observed. (b) Determine an expression for the variance of b as a function of a, conditional on x i, 0 observed. (0) For a given value of a, nd the unbiased estimator of the above class with minimum conditional variance. ((1) If a. = 0, which estimator has the smallest conditional variance? What if a = 0.5? And for a = 1? (e) Discuss the consequences of this analysis for the estimation of py by the quotient and by the regression