(1) . A researcher runs the following model using a sample size of N = 300: profit; = a + azRzi +Q3R3i + a Rai + B Innovi + u, i = 1, ...,300 where R2, R3 and Rs are the regional dummies. R21 = 1 ifi is Region2 and R21 = 0 otherwise; Rai = 1 ifi is Region3 and R31 = 0 otherwise; R = 1 ifi is Region and R = 0 otherwise, and Ru = 1 if i is not any of the above regions. It is omitted to avoid dummy variable trap; Innov is the amount of innovation in millions of dollars, and profit is the level of profit in millions of dollars. 6688 1323 218 184 0.0383 profit; = (1711) + (638) R21 (6328)R31+ + Innov (0.0115) R2 = 0.5255 Numbers in the brackets are the standard error of the corresponding coefficients. (a) What is the difference between Regionl's profit and Region2's profit? (2) (654)R (6) Is the profit difference in part (a) statistically significant? Write down the null and alternative hypothesis for a two-tailed test and carry out the relevant hypothesis test. Clearly state the statistic, critical value at 5% level of significance and your decision. (C) Interpret the coefficient of Innov. (d) What is the difference between Region3's profit and Region4's profit? (e) How would you transform model (1) to test whether there is difference between Region3's profit and Region's profit? Clearly state the null and alternative hypothesis for a two-tailed test, a feasible model for t-test involving one unknown parameter only, the t-test and the decision rule. (t) Another research finds that whether the firm has a supercomputer (PC) can help magnify the effect of Innov on profit. The variable PC is a dummy variable that equals to 1 if the company has the PC and otherwise. Clearly state a model that allows us to test the moderating effect of PC on the relationship between Innov on profit. (1) . A researcher runs the following model using a sample size of N = 300: profit; = a + azRzi +Q3R3i + a Rai + B Innovi + u, i = 1, ...,300 where R2, R3 and Rs are the regional dummies. R21 = 1 ifi is Region2 and R21 = 0 otherwise; Rai = 1 ifi is Region3 and R31 = 0 otherwise; R = 1 ifi is Region and R = 0 otherwise, and Ru = 1 if i is not any of the above regions. It is omitted to avoid dummy variable trap; Innov is the amount of innovation in millions of dollars, and profit is the level of profit in millions of dollars. 6688 1323 218 184 0.0383 profit; = (1711) + (638) R21 (6328)R31+ + Innov (0.0115) R2 = 0.5255 Numbers in the brackets are the standard error of the corresponding coefficients. (a) What is the difference between Regionl's profit and Region2's profit? (2) (654)R (6) Is the profit difference in part (a) statistically significant? Write down the null and alternative hypothesis for a two-tailed test and carry out the relevant hypothesis test. Clearly state the statistic, critical value at 5% level of significance and your decision. (C) Interpret the coefficient of Innov. (d) What is the difference between Region3's profit and Region4's profit? (e) How would you transform model (1) to test whether there is difference between Region3's profit and Region's profit? Clearly state the null and alternative hypothesis for a two-tailed test, a feasible model for t-test involving one unknown parameter only, the t-test and the decision rule. (t) Another research finds that whether the firm has a supercomputer (PC) can help magnify the effect of Innov on profit. The variable PC is a dummy variable that equals to 1 if the company has the PC and otherwise. Clearly state a model that allows us to test the moderating effect of PC on the relationship between Innov on profit