(a) You have been instructed to study the relationship between economic activities (Y) and carbon emissions (X) for firms. You have assembled data for a sample of 32 countries, where Y, is economic activities of the i-th country and X; is carbon emissions of the i-th country. Your research assistant has used the sample data to estimate the following OLS sample regression equation, where the figures in parentheses below the coefficient estimates are the estimated standard errors of the coefficient estimates: Y, = 293.111 +0.3918X; + (i = 1, ..., N) N = 32 (45.198) (0.0697) Perform a test of the null hypothesis Ho: B1 = 0 against the alternative hypothesis H: B1 #0 at the 1% significance level (i.e., for significance level a=0.01). Show how you calculated the test statistic. State the decision rule you use, and the inference you would draw from the test. [Hint: Y = Bo + B,X+u] 19 Marks]