From the given regression line ,
b2 is most accurate estimator for B2
when Var[u] is small and Cov[x,z] is close to zero
Consider b2 ,the estimator for β2 , în the model yi-A+Baxi+β34+ui . În which of the...
Question 1 Consider the following model Yi = Bx; +ui (a) Derive the OLS estimator of B, ß. (6 marks] (b) Show that B is unbiased. (9 marks] (c) Find the variance of ß. [7 marks] -r.pdf
Testing the equality of two regression coefficients. Suppose that you
are given the following regression model:
Yi = β1 + β2X2i + β3X3i + ui
and you want to test the hypothesis that β2 = β3. If we assume that the ui
are normally distributed, it can be shown that
t = βˆ
2 − βˆ
3
var (βˆ
2) + var (βˆ
3) − 2 cov (βˆ
2, βˆ
3)
follows the t distribution with n − 3...
1. Suppose the data is generated by model yi = B2.+ Ej. Suppose further that E( X) = 0, var(EX) = o2 and ( yi) is iid with finite fourth moment and and are jointly normal. But you mistakenly estimate it using the following model: y = a1 + 02.1; +e, and obtain the estimated coefficient parameters. Without looking at the analysis report, determine whether the following statement is true or false. please briefly explain. (a) lê = 0 (b)...
Consider the regression model given by: Yi = βo + β1Xi + β2Zi+ ui Suppose that an econometrician wishes to test the null hypothesis given by: Ho: β1 + β2 = 1 Use this null hypothesis to specify a restricted form of the regression model (in a form that may be estimated using an OLS estimation procedure). State the equation that you could estimate as the restricted version of this model.
Consider the regression model given by: Yi = βo + β1Xi + β2Zi+ ui Suppose that an econometrician wishes to test the null hypothesis given by: Ho: β1 + β2 = 0 Use this null hypothesis to specify a restricted form of the regression model (in a form that may be estimated using an OLS estimation procedure). State the equation that you could estimate as the restricted version of this model.
1. Consider the following multiple regression models Y βι + β2 X2i + β3 X3i + ui (1) Population regression model Yb1 b2 X2i+ b3 X3 + ei (2) Sample regression model a) Express the sample model in a deviation form. b) Using the OLS method, derive in details b2 and bs using the matrix method and Cramer's Rule.
1. Consider the following multiple regression models Y βι + β2 X2i + β3 X3i + ui (1) Population regression model...
QUESTION 17 For a given sample in the linear model, an estimate (computed from a certain estimator for B2), in general, is: A not B2 B. close to B2 c.very likely (high probability) to be close to B2. OD. none of the above. QUESTION 18 In the linear model, Cov( x, u) has the same value as: O A X*u. OB. E(X*u). OC. u. OD. none of the above. QUESTION 19 In the linear model, which of the following CANNOT...
Consider the linear model: Yi = α0 + α1(Xi − X̄) + ui.
Find the OLS estimators of α0 and α1. Compare with the OLS
estimators of β0 and β1 in the standard model discussed in class
(Yi = β0 + β1Xi + ui).
Consider the linear model: Yį = ao + Q1(X; - X) + Ui. Find the OLS estimators of do and a1. Compare with the OLS estimators of Bo and B1 in the standard model discussed in...
Consider the model yi = β0 +β1X1i +β2X2i +ui . We fail to reject the null hypothesis H0 : β1 = 0 and β2 = 0 at 5% when: a) A F test of H0 : β1 = 0 and β2 = 0 give us a p value of 0.001 b) A t test of H0 : β1 = 0 give us a p value of 0.06 and a t test of H0 : β2 = 0 a p value...
Question 1 Consider the following model Yi = B.z; + u (a) Derive the OLS estimator of B, B. (6 marks] (b) Show that is unbiased. [9 marks] (c) Find the variance of B. [7 marks]