Question

In: Economics

QUESTION TWO Consider the model:                                     Yi=β1+

QUESTION TWO

Consider the model:                                     Yi=β1+β2X1+Ui

  1. Explain all the terms included in the model above
  2. Given the model above, state the way econometricians proceed in their analysis of an economic problem?     
  3. Explain the importance of Ui in this model?What are the four reasons for the inclusion of this error term in the regression model?
  4. What is the difference between the disturbance term and the residual term?
  5. Explain the meaning of statistical inference?
  6. State the ten assumptions of the classical linear regression model and give algebraic illustrations [ if applies]
  7. State the Gauss-Markov theorem.
  8. Consider the regression models below, indicate which ones are linear in parameters or variables or both:
  1. Yi=β1+1β2Xi+ui                                                                           
  2. Yi=β1+1β2Xi2+ui

Solutions

Expert Solution

Error term is same as disturbance term.


Related Solutions

Consider a simple linear model Yi = β1 + β2Xi + ui . Suppose that we...
Consider a simple linear model Yi = β1 + β2Xi + ui . Suppose that we have a sample with 50 observations and run OLS regression to get the estimates for β1 and β2. We get βˆ 2 = 3.5, P N i=1 (Xi − X¯) 2 = 175, T SS = 560 (total sum of squares), and RSS = 340 (residual sum of squares). 1. [2 points] What is the standard error of βˆ 2? 2. [4 points] Test...
Consider a simple linear model: yi = β1 + β2xi + εi, where εi ∼ N...
Consider a simple linear model: yi = β1 + β2xi + εi, where εi ∼ N (0, σ2) Derive the maximum likelihood estimators for β1 and β2. Are these the same as the estimators obtained from ordinary least squares? Is there a reason to prefer ordinary least squares or maximum likelihood in this case?
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui...
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui . 1. [3 points] What are the assumptions of this model so that the OLS estimators are BLUE (best linear unbiased estimates)? 2. [4 points] Let βˆ 1 and βˆ 2 be the OLS estimators of β1 and β2. Derive βˆ 1 and βˆ 2. 3. [2 points] Show that βˆ 2 is an unbiased estimator of β2.
1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and...
1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=21.0213; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950.According to these results the relationship between C and Y is: A. no relationship B. impossible to tell C. positive D. negative 2. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this...
Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and get...
Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The following values are relevant for assessing goodness of fit of the estimated model with the exception of A. 0.130357 B. 8.769363 C. 1.46693 D. none of these
1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and...
1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2952 B. 2948 C. 2 D. 2950 2. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS...
Consider 2 models: yi = β1 + β2xi + ei (1) Y = X0β + e;...
Consider 2 models: yi = β1 + β2xi + ei (1) Y = X0β + e; (2) where Equation (1) represents a system of n scalar equations for individuals i = 1; ...; n , and Equation (2) is a matrix representation of the same system. The vector Y is n x 1. The matrix X0 is n x 2 with the first column made up entirely of ones and the second column is x1; x2; ...; xn. a. Set...
1. To see if the variable Xi2 belongs in the model Yi=β1+β2Xi+ui, Ramsey’s RESET test would...
1. To see if the variable Xi2 belongs in the model Yi=β1+β2Xi+ui, Ramsey’s RESET test would estimate the linear model, obtaining the estimated Yi values from this model [i.e., Yi=β1+β2Xi ] and then estimating the model Yi=β1+β2Xi+α3Yi2+ui and testing the significance of α3. Prove that, if α3 turns out to be statistically significant in the preceding (RESET) equation, it is the same thing as estimating the following model directly: Yi=β1+β2Xi+β3Xi2+ui
Question 1: Consider the simple regression model: !Yi = β0 + β1Xi + ei (a) Explain...
Question 1: Consider the simple regression model: !Yi = β0 + β1Xi + ei (a) Explain how the Ordinary Least Squares (OLS) estimator formulas for !β̂ and !β̂ are derived. (b) Under the Classical Linear Regression Model assumptions, the ordinary least squares estimator, OLS estimators are the “Best Linear Unbiased Estimators (B.L.U.E.).” Explain. (c) Other things equal, the standard error of β! ̂ will decline as the sample size increases. Explain the importance of this. Question 2: Consider the following...
1. Consider the model Yt = β1 + β2X2t + β3X3t + ut and we suspect...
1. Consider the model Yt = β1 + β2X2t + β3X3t + ut and we suspect that the variance of the error term has the following form: Var(ut) = δ1 + δ2Yt-1 + δYt-2 (a) Sketch the test proecedure for the presence of heteroskedasticity in this form. (b) Write out the GLS model.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT