1. Suppose that you have the following model and data to estimate the following equation; Nobs Y X2 X3 1 3. 2 2. 2. 3. 4. 5. 2. 4 4. 5. 3. 3. 4 2 5 Y, = A +B,X, + BX, +u, | Find the OLS estimators for the parameters using the matrices above. (35p)
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- For b there are two cases and for c I have to plug the initial data into the odeWhich of the following processes (Xt)t is weakly stationary? A: Xt = 1:6 + Xt 1 + V tB: Xt = 0:6 Xt-1 +V tC: Xt = 0:8 Xt-1 + V tD: Xt = 0:8 t + 0:6 V t – 1 The term (t) is always assumed to be white noise with variance oneConsider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.
- Find the production schedule for the technology matrix and demand vector given below: A= 0.1 0.3 0 D= 9 0.1 0.2 0.1 6 0.2 0.2 0.1 8 X= ? ? ?A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next customSuppose you are interested in the causal effect of Xi on Yi and Yi = α + βXi + ϵi. Moreover, cov(Xi , ϵi) = 0. However, you do not observe Yi . Instead, you only observe a proxy for Yi . Denote this proxy Y'i and assume it is related to Yi as follows: Y'i = Yi + µi where cov(µi , ϵi) = cov(µi , Xi) = 0. Suppose you regress Y'i on Xi . Would the resulting coefficient β' provide an unbiased estimate of β?
- Below is the answers to problem 1 and 2, please help with problem 3. Problem 1 Use the svd() function in MATLAB to compute , the rank-1 approximation of . Clearly state what is, rounded to 4 decimal places. Also, compute the root-mean square error (RMSE) between and . Solution: %code %Define matrix A A = [1, 2, 3; 3, 3, 4; 5, 6, 7]; %Compute SVD of A [U, S, V] = svd(A); %Rank-1 approx A1 = U(:,1) * S(1,1) * V(:,1)'; RMSE = sqrt(mean((A(:) - A1(:)).^2)); %Display A1 rounded to 4 decimal places disp(round(A1, 4)); 1.7039 2.0313 2.4935 2.7243 3.2477 3.9867 4.9087 5.8517 7.1832 %Display RMSE disp(RMSE); 0.3257 Problem 2 Use the svd() function in MATLAB to compute , the rank-2 approximation of . Clearly state what is, rounded to 4 decimal places. Also, compute the root-mean square error (RMSE) between and . Which approximation is better, or ? Explain. Solution: %code A = [2, 4, 7; 3, 3, 5; 1, 6, 6]; % Compute SVD of A [U, S, V] = svd(A); % Rank-2…1. In a case where f'(x) is required for f(x1) when the datapoints available are x0 and x1. Which method is best used? 2. In modified Euler'a method, the predictor is computed similar with: __ 3. In order to multiply matrices, they should be __.This is a multipart question 6.) Diesel Dave has modified his massive truck to combat global cooling, and to roll coal on his neighbor Environmentalist Ed. With each blast of diesel exhaust fumes, Diesel Dave releases sulfur dioxide in a giantblack cloud. Every morning as Diesel Dave is leaving home he rolls coal into Environmentalist Ed's yard. Not surprisingly, Environmentalist Ed is diligently collecting data on the air quality in his yard. Suppose Diesel Davereleases sulfur dioxide in a normally distributed manner with a mean of 2800 ppm and a standard deviation of 120 ppm. What is the probability that on a random morning he will release sulfur dioxide greater than 3000ppm? Suppose in order to sue Diesel Dave, Environmentalist Ed needs the daily average level of sulfur dioxide emissions to exceed 3000 ppm. However, he can choose to take his mean measurement over 2, 3, or 15 days. Which number of days would maximize Environmentalist Edís chances of suing Diesel Dave? (Hint: What…
- The following are smoke readings taken on two different camshafts: Engine Camshaft A Camshaft B A 2.7 2.6 B 2.9 2.6 C 2.9 3.2 D 3.5 3.3 Conduct Wilcoxon signed-rank test to test H0: the one-side alternative.How will you choose between following non-nested competing models:- Md=Beta lag (0)+ beta lag(1) Y+ V and Md= alpha lag(0) + alpha lag(1) i+ UYou are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. X Y Z A 48 20 63 B 38 33 21 Give all answers rounded to 3 places after the decimal point, if necessary. (a) Enter the expected frequencies below: X Y Z A B To find the expected frequencies: Enter the observed matrix into the calculator, per the Technology Corner. Perform the test, per the Technology Corner. Return to the matrix menu and view the B matrix. This will be the expected frequencies. (b) What is the chi-square test-statistic for this data? Test Statistic: χ2= (c) What is the critical value for this test of independence when using a significance level of α = 0.005? Critical Value: χ2= (Enter 10.597 as the answer to this question.) (d) What is the correct conclusion of this hypothesis test at the 0.005 significance level? There is sufficient evidence to support the claim that…