. Explain the attached questions below.

1. [42 points] Suppose that you have an iid random sample {Xi, Y} of three data points (X1, Yl) = (0, 0) ; (X2, Y2) = (2,3); (X3, Y3) = (4,3). (a) (2 point) Calculate the sample mean of X; and Yi. (b) (6 points) You run a simple linear regression of Y, on Xi. Calculate the OLS estimates of the slope and intercept. (c) (3 points) Calculate the predicted value and residuals for each of three data points. (d) (6 points) Calculate the TSS, ESS and SSR. (e) (4 points) Check whether TSS=ESS+SSR and interpret the equation. (f) (3 points) Calculate the R for the regression. (g) (3 points) Interpret R2 in words. (h) (4 points) Calculate the sample covariance between the residuals and Xi, which is defined in general as 1 Et-, (Xi - X)(ui - u), where n is the sample size and u; is the residual. (i) (4 points) Calculate the sample covariance between the residuals and predicted value, which is defined in general as I EL, (Yi - Y)(ui - u), where n is the sample size and Y; is the predicted value. (j) (4 points) Draw a graph to show (1) the three data points (2) the estimated regression line and (3) their residuals. (k) (3 points) Draw the point (X, Y) in the graph above and explain why the point (X, Y) is always on the regression line.1. Consider a competitive exchange economy with two consumers and two goods. Suppose that consumer i has initial endowments wi = (wj, w2), where w; > 0, i = 1, 2 and j = 1, 2. His preferences are given by the following utility function: U' = aln(x;) + (1 -a) In(x2), where 0