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e. (4p) Suppose that the Phillips Curve (PC) relationship for this economy is given by: The - 7f= -1(ut - un) Express the PC relationship above as a function of output gap, Yt - In . f. (4p) What is the current inflation rate, I, for this economy?1. Let R be the region in the plane bounded by the y-axis and the graphs of y = |2m| and y = 3 + 2:. (a) Set up an integral or integrals to represent the volume of the solid obtained by revolving R around the :r-axis. You do NOT need to evaluate your integrals(s). (b) Set up an integral or integrals to represent the volume of the solid obtained by revolving R around the line 9 : -2. You do NOT need to evaluate your integrals(s). (c) Set up an integral or integrals to represent the volume of the solid obtained by revolving R around the line 3 = 4. You do NOT need to evaluate your integrel(s). 2. A rod of length 2 meters has mass density _ E 9(w)72+5$m at a distance 3 meters from one end. (3} Find the center of mass of the rod. (b) At What point should the rod be separated so that the two separate pieces have the same mass? (c) Explain why the result of part (b) is not the center of mass of the rod. 3. Verify the formula gwra for the volume of a sphere by treating the sphere as the solid obtained by revolving the top half of a circle of radius 'r around the x-axis. Recall that the equation of a circle centered at the origin with radius r is $2 + y2 : 1'2. Note that r is a constant. (To verify means to exactly evaluate the integral.) 1. For which violation of the classical linear regression assumption does Durbin-Watson test is used for detection? And outline the procedure for the test merely formulating the hypotheses and stating the decision rule using the measure of autocorrelation, p, and the Durbin-Watson statistics, d-statistics. 2. The economic theory of investment states that investment expenditure at a given point in time (I) is negatively affected by interest rate at a given point in time (r). Suppose that the functional relationship in the stated economic theory is linear and estimated values of the intercept and slope are 82 and 0.6 respectively. Based on the stated economic theory and the associated information, derive the estimated econometric model and predicate the value of the dependent variable provided that 50 is given as value of the independent variable. 3. The following estimated equation was obtained by OLS regression using quarterly data for 1978 to 1996 inclusive. Y, = 2.20+0.104X, (3.4) (0.005) Standard errors are in parentheses, the explained sum of squares and the residual sum of squares were 109.6 and 18.48 respectively. Thus, a) Test a 5% level of significance for the statistical significance of the parameter estimates using t-test technique b) Test the overall test of significance ant 1% c) Calculate the coefficient of determination 4. Consider the following estimated regression model of monthly earnings of 25 employees selected at random from the pool of employees in a given organization. Assuming the monthly earning (ME) is affected by two explanatory variables-SEX and AGE of employees, the regression output is given as ME = -1.65+ 0.33SEX +0.4 AGE (-0.60) (0.18) (0.03) R' = 0.825 Given the standard errors of each estimate in brackets answer the following questions A. Test the statistical significance of the intercept using standard error test B. Test the statistical significance of SEX at 5% level of significance C. Test the overall significance of the model at 1% level of significance D. Interpret R21. A bit of practice with dummy variables and heferoskedasficify: Consider the following model for the logarithm of wage given years of university education and gender of person 1' : log(wage;) = g + oqfenmle, + lronmi; + lfemale; x 10mm,- + u; # where log is the natural logarithm, femlei is a dummy variable that is equal to 1 if person i is female is 0 otherwise, and 10mm",- is the number of years of university education that person 1' has. Based on a random sample of 6763 individuals, we have estimated this model using OLS and obtained the following estimated equation: _--_-__-_ log(wage,z) =3.289 0.360fenmle; +0. 050 forum,- +0.0309maie, x forum}, (0011) (0.015) (0.003) (0.005) 1':l,2,...,67l63,1l22 = 0.202. a. Explain how you would test the hypothesis that the conditional expectation of log(wage) conditional on years of university education is exactly the same for men and women. You need to specify the null and the alternative, the test statistic and its distribution under the null, the regression that you should run so that you can compute the test statistic, and the rule for rejection or non-rejection of the null hypothesis. c. Using the estimated equation, nd the value of tomni (total number of years in university) such that the predicted values of log(wage) are the same for men and women. Can women realistically get enough years of university education so that their earnings catch up to those of men? Explain. d. Suppose we suspect that the variation of Iog(wage) around its conditional mean is larger for women than it is for men. That means that in the