Suppose the error variance of a model is describe by the equation σt2 = α0 +...
Suppose the error variance of a model is describe by the equation σt2 = α0 + α1 Z1 + α2Z2 + εt Describe how to use Feasible Generalized Least Squares to get efficient estimates of the coefficients of the model.
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Suppose the error variance of a model is describe by the
equation σt2 = α0 +...
Question 1 (a) (4 points) What are they key advantages of the Logit model over the...
Question 1 (a) (4 points) What are they key advantages of the Logit model over the Linear Probability Model? (b) (15 points) In class we saw that efficient estimates of the coefficients from a linear regression model can be obtained under the presence of heteroskedasticity using Generalized Least Squares (GLS). How does GLS work? That is, describe the mechanism through which GLS addresses non-constant error variances to achieve efficient estimation. (c) (5 points) Let Zi be the log-odds ratio in...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X?...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X? a. In this case, would an ordinary least squares regression provide you with the best b. c. linear unbiased estimates? Why or why not? What is the transformed model that would give you constant error variance? Given the following data: y = (4,3,1,0,2) and x = (1,2,1,3,4) Find the generalized least squares estimates of β1 and β2 (Do this by hand! Not with excel)
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming a conditional variance function Varux=σ2h(x). Which of the following statements is correct? A) The function h(x) does not need to be estimated as part of the procedure B) If the assumption about the conditional variance of the error term is incorrect, then FWLS is still consistent. C) FWLS is the best linear unbiased estimator when there is heteroscedasticity. D) None of the above answers...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the OLS estimator for {00, Bo}, the minimizer of E. (Y: - a - 3x), is . (X.-X) (Y-Y) and a-Y-3X. - (Xi - x) When the equation (1) is the true data generating process, {X}- are non-stochastic, and {e} are random variables with B (ei) = 0, B(?) = 0, and Ele;e;) = 0 for any i, j = 1,2,...,n and i j, we...
Linear Algebra Question 25. Suppose you are looking at data which is supposed to fit an...
Linear Algebra Question
25. Suppose you are looking at data which is supposed to fit an exponential equation, i.e. a model of the form y= Cekz where C and k are constants. Suppose your data points are (2, 5), (3,8) and (4, 17). Use least-squares to find (decimal approximations to) the values of C and k which best fit this model How to proceed: First, take the natural log of both sides of the model to obtain what is called...
1. Table of descriptive statistical measures (arithmetic mean, standard deviation, smallest value and largest value) for the variables in the model with a detailed discussion of the table 2. The equation is in the community form of the model you reached,
1. Table of descriptive statistical measures (arithmetic mean, standard deviation, smallest value and largest value) for the variables in the model with a detailed discussion of the table2. The equation is in the community form of the model you reached, then display the results of the estimated equation from the Gretl program with errors. Standard normal as well again with proper standard errors.3. Discuss and explain the results of the estimated model and then the number of reasons why the...
Coefficientsa Standardized Coefficients Beta Unstandardized Coefficients Model Std. Error Be Consant00 56 174 6.204 1.095 863 469 2.695 169 593 680 120 ACTMathScore1.051 649 279 GPA a. Dependent V...
Coefficientsa Standardized Coefficients Beta Unstandardized Coefficients Model Std. Error Be Consant00 56 174 6.204 1.095 863 469 2.695 169 593 680 120 ACTMathScore1.051 649 279 GPA a. Dependent Variable: ACTcompositescore 24. Write out the regression equation in the form of - a + math Xmath +bGPA XGPA (You can use the equation editor or write it out by hand) a. The a is the value on the "Coefficients" table in the (Constant) row and B Unstandardized Coefficients column. This is...
(a) Suppose you are given the following (x, y) data pairs
(a) Suppose you are given the following (x, y) data pairs x136y217Find the least-squares equation for these data (rounded to three digits after the decimal) (b) Now suppose you are given these (x, y) data pairs. x217y136Find the least-squares equation for these data (rounded to three digits after the decimal). (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes No (d) Solve your answer from part (a) for x (rounded to...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would comput...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would compute the parameters β | 1 . Namely, if β is the least squares solution of the system Χβ y, what are the matrix X and the right-hand side vector y? what quantity does such β minimize? (b)...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X? a. In this case, would an ordinary least squares regression provide you with the best b. c. linear unbiased estimates? Why or why not? What is the transformed model that would give you constant error variance? Given the following data: y = (4,3,1,0,2) and x = (1,2,1,3,4) Find the generalized least squares estimates of β1 and β2 (Do this by hand! Not with excel)
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the OLS estimator for {00, Bo}, the minimizer of E. (Y: - a - 3x), is . (X.-X) (Y-Y) and a-Y-3X. - (Xi - x) When the equation (1) is the true data generating process, {X}- are non-stochastic, and {e} are random variables with B (ei) = 0, B(?) = 0, and Ele;e;) = 0 for any i, j = 1,2,...,n and i j, we...
Linear Algebra Question
25. Suppose you are looking at data which is supposed to fit an exponential equation, i.e. a model of the form y= Cekz where C and k are constants. Suppose your data points are (2, 5), (3,8) and (4, 17). Use least-squares to find (decimal approximations to) the values of C and k which best fit this model How to proceed: First, take the natural log of both sides of the model to obtain what is called...
Coefficientsa Standardized Coefficients Beta Unstandardized Coefficients Model Std. Error Be Consant00 56 174 6.204 1.095 863 469 2.695 169 593 680 120 ACTMathScore1.051 649 279 GPA a. Dependent Variable: ACTcompositescore 24. Write out the regression equation in the form of - a + math Xmath +bGPA XGPA (You can use the equation editor or write it out by hand) a. The a is the value on the "Coefficients" table in the (Constant) row and B Unstandardized Coefficients column. This is...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would compute the parameters β | 1 . Namely, if β is the least squares solution of the system Χβ y, what are the matrix X and the right-hand side vector y? what quantity does such β minimize? (b)...
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