Consider a regression model where y is explained by two regressors x1 and x2, i.e. a regression of the form yi = x1i1 + x2i2 + ui (1) where i = 1, . . . , N observations are available. (a) Rewrite the model in matrix notation and derive the formula for the OLS estimator. State necessary assumptions on the regressors and the error term ui such that OLS results in unbiased estimation (start by defining unbiased). (b) Show formally that if the two regressors are orthogonal, i.e. x1i x2i = 0, the values obtained for the coefficients x1 and x2 by estimating equation (1) are identical to the coefficients obtained by performing an OLS regression of y on only x1 respectively by performing an OLS regression of y on only x2. HINT: Use matrix notation for the orthogonality condition! (c) Give a geometric interpretation of the result established in b).