b) Perform zero null hypotheses for each of the three parameters in the above model using a = 5%and clearly state your deductions as well as the alternate hypotheses.c) Determine 95% confidence intervals for the parameters of the model and c-".your deductionsfor part (b) above.d) What is the p-value for each parameter with respect to a zero null hypothesis. 7. a) Suppose we have the following data for a Cobb-Douglas production function, including itsstochastic term i.e.:Y, = B,x: xeWhere Y=outputX2 = labour inputХз — саpital inputu = stochastic disurbance termhas been collected:BENGO019Coursework on Probability, Statistics and RegressionPage | 3YearReal gross productLabour daysReal capital input(millions of NT $)", Y (millions of days) X2(millions of NT $), X3195816,607.7275.517,803.7195917,511.3274.418,096.8196020,171.2269.718,271.8196120,932.9267.019,167.3196220,406.0267.819,647.6196320,831.6275.020,803.5196424,806.3283.022,076.6196526,465.8300.723,445.2196627,403.0307.524,939.0196728,628.7303.726,713.7196829,904.5304.729,957.8196927,508.2298.631,585.9197029,035.5295.533,474.5197129,281.5299.034,821.8197231,535.8288.141,794.3Source: Thomas Pei-Fan, "Economic Growth and Structural Change in Taiwan". 1952-1972, A Production function Approach" unpublishedPhD thesis, Dept of Economics, Graduate Center, City University of New York 1976, Table Il*New Taiwan dollars.Show using MOLS (and an appropriate software package, or you may write code yourselves usingany programming language of your choice) that the data above gives rise to the following model (theterms in the second row are the standard errors), calculate all the standard errors and t-values.InY, = -3.3384 +1.4988ln(X2) + 0.48991 n(X)(2.4495) (0.5398)(0. 1020)t = (-1.3629) (2.7765)R? = 0, 8890, df = 12(4. 8005)R2 = 0.8705 (you do not need to calculate this)

Given: Year Real gross product (millions of NT $)°, Y Labor days (millions of days) X2 Real…

Answered: 7. a) Suppose we have the following…

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4. Assume that a risk-free money market account is added to the market described in Q2. The continuously compounded rate of return on the money market account is 0% per period. (i) Use the method of Lagrange multipliers to determine the proportions of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. Your answer must express the proportions as a function of µ. (ii) Recall that the market portfolio has highest Sharpe ratio. Formulate the optimi- sation problem which characterises the market portfolio. You don't have to solve this optimisation problem.
4. I was able to convince the plan manager to allow me to make the change to the larger production plant. My job's on the line now! So I am monitoring it pretty closely. Here are the results for the day: Table 4. Production rate from pilot plant demonstration tests. Run # 1 2 3 4 5 P (pounds per hour) 2200 2200 2300 2200 2300 From these data, please estimate: a. Estimate the Type A uncertainty in these measurements. Be sure to include the units. b. Estimate the Type B uncertainty associated with these measurements. Be sure to include units. C. Determine the uncertainty in the measurement of pressure in the cylinder. Be sure to include units. State your answer as average +/- uncertainty.
6.
17. A risk manager would like to simulate the price of a stock using the discretized GBM, where St+At = St + µS{At+√Ã£$£€ where μ and o denote, respectively, the stock annual mean return and annual volatility. The data suggest that the weekly mean return on the stock is 0.5% and the weekly volatility is 4%. Assuming a weekly time step of At = 1/52 (in terms of annual units), what is the appropriate estimate of μ? (a) = 26.4% (b) û = 30.16% (c) û = 4.5% (d) û = 17.94% 18. Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift μ = 0.01 and an annual volatility of o= 0.25. If today's price is $100, what is the probability that the price two years from now will drop below $80? Hint: Recall that under GBM, the future price at T, i.e. ST, given today's spot price, St, is with TT-t and €~ = (a) 21.51% (b) 35.48% (c) 51.1% (d) 30.47% ST= St x exp (μ x exp [(μ-27 ) XT + √F X 0 Xe] N (0, 1).
10
9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
Suppose there are three fare classes in an airline fares p1 = $300, p2 = $200, and p3 = $100. You want to utilize the EMSR-b heuristic to calculate the protection level for classes 1 and 2 together. The demand distribution for class 1 is Normal with mean 50 and standard deviation 5. The demand distribution for class 2 is Normal with mean 75 and standard deviation 12. What is the price for the virtual class 1-2 under EMSR-b?
13. A researcher estimates the following regression model: Yt = a + ßxt + Ut where yt and xt are both non-stationary variables. Which of the following statements is correct? a) This necessarily leads to spurious results b) The Durbin-Watson d statistic will be larger than the R² c) Including a time trend in the regression specification will provide meaningful results d) Differencing both variables may provide meaningful results but could lose some useful information
7

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7. a) Suppose we have the following data for a Cobb-Douglas production function, including its stochastic term i.e.: Where Ymoutput X2 = labour input X = capital input