Testing the equality of two regression coefficients. Suppose that you are given the following regression model: Yi = β1 + β2X2i + β3X3i + ui
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 df (see Section 8.6). (In general, for the k-variable case the df are n − k.) Therefore, the preceding t test can be used to test the null hypothesis β2 = β3. Apply the preceding t test to test the hypothesis that the true values of β2 and β3 in the regression (C.10.14) are identical. Hint: Use the var-cov matrix of β given in (C.10.9).
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Testing the equality of two regression coefficients. Suppose that you are given the following regression model: Yi = β1 + β2X2i + β3X3i + ui
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 and βˆ be the OLS estimators of β and β . Derive βˆ and βˆ. 12 1212 3. [2 points] Show that βˆ is an unbiased estimator of β .22
Consider the regression model given by: Yi = βo + β1Xi + β2Zi+ ui Suppose that...
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...
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.
The following table gives data on output and total cost of production of a commodity in the short run To test whether the preceding data suggest the U-shaped average and marginal cost curves typically encountered in the short run, one can use the followin
The following table gives data on output and total cost of production of a
commodity in the short run. (See Example 7.4.)
Output Total cost, $
1 193
2 226
3 240
4 244
5 257
6 260
7 274
8 297
9 350
10 420
To test whether the preceding data suggest the U-shaped average and
marginal cost curves typically encountered in the short run, one can use
the following model:
Yi = β1 + β2Xi + β3X2
i...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...
Help Please? 3) Given a relationship of the form Yi-β1 + β2Xi + ui , where...
Help Please?
3) Given a relationship of the form Yi-β1 + β2Xi + ui , where ui is white noise a) Show that Var(Y) 2 and that CoY, Y0 b) Given the OLS formula for B , find a set of non-random weights ci such that can be expressed as Σ¡Yi 1 problem 3 and the results of part a above to show thatthe variance ofa isequal too5xT
Consider the model yi = β0 +β1X1i +β2X2i +ui . We fail to reject the null...
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...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...
In a multiple regression analysis, k = 5 and n = 26, the MSE value is...
In a multiple regression analysis, k = 5 and n = 26, the MSE value is 9.99, and SS total is 402.22. At the 0.05 significance level, can we conclude that any of the regression coefficients are not equal to 0? (Round your answers to 2 decimal places.) H0: β1 = β2 = β3 = β4 = β5 = 0 H1: Not all β's equal zero. 1) DF1= 2) DF2= 3) Ho is rejected if F > = 4) Regression...
In the simple linear regression with zero-constant item for (xi , yi) where i = 1, 2, · · · , n, Yi = βxi + i where {i} n i=1 are i.i.d. N(0, σ2 ). (a) Derive the normal equation that the LS estimator...
In the simple linear regression with zero-constant item for (xi , yi) where i = 1, 2, · · · , n, Yi = βxi + i where {i} n i=1 are i.i.d. N(0, σ2 ). (a) Derive the normal equation that the LS estimator, βˆ, satisfies. (b) Show that the LS estimator of β is given by βˆ = Pn i=1 P xiYi n i=1 x 2 i . (c) Show that E(βˆ) = β, V ar(βˆ) = σ...
Help Please?
3) Given a relationship of the form Yi-β1 + β2Xi + ui , where ui is white noise a) Show that Var(Y) 2 and that CoY, Y0 b) Given the OLS formula for B , find a set of non-random weights ci such that can be expressed as Σ¡Yi 1 problem 3 and the results of part a above to show thatthe variance ofa isequal too5xT
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