2. Consider the following model: Bo where y is a (nx1) vector containing observations on the dependent variable, B = B B y = XB+u X'X = X is a (n x 3) matrix. The first column of X is a column of ones whilst the second and third columns contain observations on two explanatory variables ( and 2 respectively). u is (n x 1) vector of error terms. The following are obtained: (X'X)- 192.0 259.6 1153.1 259.6 402.8 1371.1 1153.1 1371.1 8107.6 0.2792 -0.1055 -0.0219 -0.1055 0.0457 0.0073 -0.0219 0.0073 0.0020 1234.718 X'y = 1682.376 7345.581 =0.08069, where is standard error of the regression. (a) (i) How many observations are there, i.e. what is the value of n? (2) (ii) Calculate the OLS estimates of 3, and the standard error of $. [2 MARKS] [10 MARKS] (b) For each of the following hypothesis tests, clearly state the null and alternative hypotheses, the test statistic and its distribution, the decision rule, and your conclu- sions. Use a 5% significance level in both cases. (i) Test the null hypothesis that explanatory variable has no effect on the de- pendent variable y. [5 MARKS] (ii) The R from the OLS regression of model (2) is 0.7763, test the overall signif- icance of the regression.