(a) (b) In a private boarding school, there are three separate classes (A, B and C) for the 4-"1L grade. Mark has obtained data on test scores for each of the four classes. Class C has lower number of students compared to class A and B. Mark attempts to run the following regression: Y: = 130+ 51x1: + 13239: + 3X3,+u.. where Y, is the test scores. X, is a dummy variable that takes the value of I if class A and '0' otherwise. X2 is the is a dummy variable with value of 1 if class B and 0 otherwise, and X3 is a dummy variable with value of I if class C, and 0 otherwise. However, Mark' 5 regression software is unable to run the regression. An error message states that above equation cannot be estimated. Why does this issue occur and what is the potential solution? (4 marks) Based on the following output, determine whether the series is normally distributed. Clearly state the null hypothesis, p-value and conclusion. Assume the level of significance is 1%. (6 marks) Series: SPREAD Sample 1986M03 2007M04 Observations 254 Mean 0.391654 Median 0.360000 Maximum 1 .500000 Minimum 0.550000 Std. Dav. 0.233391 Skawriass 0.01 8696 Kurtcsis 2.432459 JarquaBera 19.03929 Probability 0.0000T3 (C) (d) ECON339 (FAA) i' Page 5 of 6 Why is it necessary to include an error correction term in the model instead of using a first difference model (dy: = ax: + w}? Discuss your answer with the relevant workings. Clearly show a model with an error correction term. (8 marks) Suppose two variables are integrated of different orders. Briefly explain whether cointegration test should be performed. (2 marks)