II. Applications [60 points total] 1 d a b - Note:Ce T' - ada berita = d - bcL- A. [12 points] The following problems related to basic linear algebra and statistics are independent with each other. (a) 2*3+4*5+2*3 can be expressed as a multiplication of two vectors. What are the two vectors? (b) If you have a sample of {4, 3,2}, compute the mean and standard deviation (c) The midterm election is coming, and to a large extend, the future market performance depends on which party becomes majority in the House. Historically, the market return was 5% a year after an Republicans take the majority, and 3% if the Democrats keep the majority. Suppose you are predicting that the likelihood for the Democrats to win is 70%, what market return would you expect to see next year? (d) If the estimated univariate model is given as y = 3 + 2 x+ u, and = 1.5, y = 6, what should be the average of estimated residuals? In this section, you need the following critical values at a a=5% significant level: Df 60 >120 ta, DF: 1.67 1.66 ta/2, Df: 2.00 1.98 Fa, 1,DE: 4.00 3.92 Fa, 2.DE: 3.15 3.07 The test statistics for a single restriction and the joint test are: (RB-9) (.'. - '@)/J F = Vs?[R(X'X) 'R'] '/(n - K) t= Fj,n-K II. Applications [60 points total] 1 d a b - Note:Ce T' - ada berita = d - bcL- A. [12 points] The following problems related to basic linear algebra and statistics are independent with each other. (a) 2*3+4*5+2*3 can be expressed as a multiplication of two vectors. What are the two vectors? (b) If you have a sample of {4, 3,2}, compute the mean and standard deviation (c) The midterm election is coming, and to a large extend, the future market performance depends on which party becomes majority in the House. Historically, the market return was 5% a year after an Republicans take the majority, and 3% if the Democrats keep the majority. Suppose you are predicting that the likelihood for the Democrats to win is 70%, what market return would you expect to see next year? (d) If the estimated univariate model is given as y = 3 + 2 x+ u, and = 1.5, y = 6, what should be the average of estimated residuals? In this section, you need the following critical values at a a=5% significant level: Df 60 >120 ta, DF: 1.67 1.66 ta/2, Df: 2.00 1.98 Fa, 1,DE: 4.00 3.92 Fa, 2.DE: 3.15 3.07 The test statistics for a single restriction and the joint test are: (RB-9) (.'. - '@)/J F = Vs?[R(X'X) 'R'] '/(n - K) t= Fj,n-K