QUESTION 4 Which one of the following statements is true for a linear regression model with non-spherical disturbances (i.e. E(uu') = Q): O The GLS estimator covariance matrix is unreasonable. The OLS estimator is not consistent. The standard formula for the OLS estimator covariance matrix is incorrect. The GLS estimator is not consistent. O All of the above. None of the above.
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- Describe the important characteristics of the variance of a conditional distribution of an error term in a linear regression. What are the implicationsfor OLS estimation?8. Which of the following best describes the linear probability model? The model is the application of the linear multiple regression model to a binary dependent variable The model is an example of probit estimation The model is another form of logit estimation The model is the application of the multiple regression model with a binary variable as at least one of the regressors OO1.1 Which of the following is NOT a good reason for including a disturbance term in a regression equation?/ A. To allow for random influences on the dependent variable/ B. To allow for errors in the measurement of the dependent variable/ C. It captures omitted determinants of the dependent variable D. To allow for the non-zero mean of the dependent variable/ 1.2 Consider the equation Y = B1 + B2X2 + u. A null hypothesis of H0: B2 = 0 means that/ A. X2 has no effect on the expected value of Y / B. B2 has no effect on the expected value of Y/ C. X2 has no effect on the expected value of B2 / D. Y has no effect on the expected value of X2/ 1.3 The OLS residuals in the multiple regression model/ A. can be calculated by subtracting the fitted values from the actual values / B. are zero because the predicted values are another name for forecasted values / C. are typically the same as the population regression function errors / D. cannot be calculated because there…
- "In the regression model InY=b0+b1*InX+u, the coefficient b1 is interpreted as" O the intercept O A covariance O A regressor O An elasticityAs an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 4.5 3.5 3 2.5 1.5 1 0.5 6. 10 12 14 16 18 Percentage of drivers under age 21 Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear…An OLS regression should be used when the independent variable is nominal. A. True B. False
- 5 We are given a sample of n observations which satisfies the following regression model: yi = β0 + β1xi1 + β2xi2 + ui , for all i = 1, . . . , n. This model fulfills the Least-Squares assumptions plus homoskedasticity. (a) Explain how you would obtain the OLS estimator of the coefficients {β0, β1, β2} in this model. (You do not need to show a full proof. Writing down the relevant conditions and explain)1. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearity5. In classical linear regression model, Var (u) = o² refers to the assumption of Zero mean value of disturbance term a. b. Homoscedasticity c. No autocorrelation
- QUESTION 1 Which one of the following assumptions is known as the spherical disturbance assumption? E(uu') = 0 E(uu') = XXxy1 E(uu') = =o²xy E(uu') = a2 All of the above. None of the above. QUESTION 2 If the error term covariance matrix is not spherical, but it is diagonal, then you have: O Autocorrelation, but no heteroskedasticity. O Heterskedasticity and autocorrelation. Heteroskedasticity, but no autocorrelation. Both heteroskedasticity and autocorrelation. Neither hetroskedasticity or autocorrelation. QUESTION 3 Which one of the following statements is true for a linear regression model with non-spherical disturbances (i.e. E(uu') = Q): The GLS estimator is inefficient. The OLS estimator is inefficient. The OLS estimator covariance matrix is diagonal. The GLS estimator covariance matrix is block-diagonal. All of the above. None of the above.2 of 3 2. (a) Consider the generalized linear regression model Yt = a + Bxt + Et. 4 Assume Est = 0 and that we have no serial correlation among the disturbances but More var(t) = σ²x², where we assume that xt 0 for all t. Derive the feasible GLS estimator of a and B. Now consider the following regression, setting == / 7 It 1 Xt and estimate a and B again. How would the estimates differ from GLS. Explain. Yt =a Consider the ARMA(1.1) process : +B+ εi,QUESTION 2 Consider the following bivariate linear regression model y = a+3x+u. Suppose that E[u]x] #0 and that z is a valid instrument for r. Knowing that Cov(y, z) = 0.5 and Cov(z, x) = 0.5, the IV estimate of 3 is 1. %3D O True O False