Econometrics Question: Consider the data generating process Y= β1+ β2Xi+β3Zi+β4Wi+β5Pi+β6Ti+e e~N(0, σ^2) and the null hypothesis...
Econometrics Question:
Consider the data generating process Y= β1+ β2Xi+β3Zi+β4Wi+β5Pi+β6Ti+e e~N(0, σ^2)
and the null hypothesis Ho: β4=5 and β2+β3=0 and 2β5-4β6=0.
Discuss how you would test the null hypothesis Ho: β2/β3=4 against Ha: β2/β3≠4.
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Econometrics Question:
Consider the data generating process Y= β1+
β2Xi+β3Zi+β4Wi+β5Pi+β6Ti+e e~N(0, σ^2)
and the null hypothesis...
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...
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...
Econometrics 13) Consider the classical linear regression model y = XB + E, EN(0,021) The data...
Econometrics
13) Consider the classical linear regression model y = XB + E, EN(0,021) The data are collected in such a way that the X matrix is orthogonal, that is X'X = 1. We want to test the null hypothesis that Ho: B1 + B2 + ... + Bx = 0. For this particular hypothesis, the standard t-test for a single linear restriction r' B = q reduces to ki bi a) t= i=1 b) t = svk Ek=1b c)t...
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...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return...
Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a...
Section 12.3 Multiple Linear Regression:
Number ONE:
Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a through h EEB Click the icon to see the software output. Data Table The regression equation is Y-1738.93 - 384.54x1 517.39x2 Predictor Constant X1 X2 Coef 1738.93 - 384.54 -517.39 SE Coef 369.06 101.65 - 3.78 0.002 353.04 - 1.47 0.162 4.71 0.000 s-172.003 R-sq-55.0% R-sq(adj):49.0% Analysis of Variance MS Source Regression Residual Error 17...
e. Consider the multiple regression model y X 3+E. with E(e)-0 and var (e) ơ21 Assume that ε ~ N(0 σ21), when we test the hypothesis Ho : βί-0 against Ha : βί 0 we use the t statistic with n-k-1 degr...
e. Consider the multiple regression model y X 3+E. with E(e)-0 and var (e) ơ21 Assume that ε ~ N(0 σ21), when we test the hypothesis Ho : βί-0 against Ha : βί 0 we use the t statistic with n-k-1 degrees of freedom. When Ho is not true find the expected value and variance of the test onsider the genera -~ 0 gains 0 1S not true find the expected value and variance of the test statistic.
e. Consider...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε to n = 30 data points and obtain SSE = 282 and R^2 = 0.8266 a.) Find an estimate of s^2 for the multiple regression model (a) s^2 ≈ 30.9856 (b) s^2 ≈ 28.6021 (c) s^2 ≈ 1.3111 (d) s^2 ≈ 29.7938 (d) b.) Based on the data information given in a.), you use F-test to test H0...
Question 2 1 pts suppose you estimate the following model: Y-α + β1 X1 + β2X2...
Question 2 1 pts suppose you estimate the following model: Y-α + β1 X1 + β2X2 + γΖ + u You wish to test the null hypothesis: Ho; A-:-As against a two-sided alternative. You do so, and get the following estimates: βι 5.23, B2--4.56, 8e (A) 2.09, 8e (%) 1.47, 8e (A-A) 2.24, 8e (A +%)-0.94 What is the value of the relevant test statistic for this hypothesis test? 4.37 0.71 0.30 10.41
10-13.. Consider the hypothesis test H0 : μι Ma against , : μ.< μ2. Suppose that sample sizes n-15 and n-15, that 7.2 and x2-7.9, and that si 4 and s 6.25. Assume that σ-σ and that the data ar...
10-13.. Consider the hypothesis test H0 : μι Ma against , : μ.< μ2. Suppose that sample sizes n-15 and n-15, that 7.2 and x2-7.9, and that si 4 and s 6.25. Assume that σ-σ and that the data are drawn from normal distribu- tions. Use α 0.05 (a) Test the hypothesis and find the P-value (b) Explain how the test could be conducted with a confidence interval. than μ2? be used to obtain B 0.05 if u, is 2.5...
Econometrics
13) Consider the classical linear regression model y = XB + E, EN(0,021) The data are collected in such a way that the X matrix is orthogonal, that is X'X = 1. We want to test the null hypothesis that Ho: B1 + B2 + ... + Bx = 0. For this particular hypothesis, the standard t-test for a single linear restriction r' B = q reduces to ki bi a) t= i=1 b) t = svk Ek=1b c)t...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return...
Section 12.3 Multiple Linear Regression:
Number ONE:
Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a through h EEB Click the icon to see the software output. Data Table The regression equation is Y-1738.93 - 384.54x1 517.39x2 Predictor Constant X1 X2 Coef 1738.93 - 384.54 -517.39 SE Coef 369.06 101.65 - 3.78 0.002 353.04 - 1.47 0.162 4.71 0.000 s-172.003 R-sq-55.0% R-sq(adj):49.0% Analysis of Variance MS Source Regression Residual Error 17...
e. Consider the multiple regression model y X 3+E. with E(e)-0 and var (e) ơ21 Assume that ε ~ N(0 σ21), when we test the hypothesis Ho : βί-0 against Ha : βί 0 we use the t statistic with n-k-1 degrees of freedom. When Ho is not true find the expected value and variance of the test onsider the genera -~ 0 gains 0 1S not true find the expected value and variance of the test statistic.
e. Consider...
Question 2 1 pts suppose you estimate the following model: Y-α + β1 X1 + β2X2 + γΖ + u You wish to test the null hypothesis: Ho; A-:-As against a two-sided alternative. You do so, and get the following estimates: βι 5.23, B2--4.56, 8e (A) 2.09, 8e (%) 1.47, 8e (A-A) 2.24, 8e (A +%)-0.94 What is the value of the relevant test statistic for this hypothesis test? 4.37 0.71 0.30 10.41
10-13.. Consider the hypothesis test H0 : μι Ma against , : μ.< μ2. Suppose that sample sizes n-15 and n-15, that 7.2 and x2-7.9, and that si 4 and s 6.25. Assume that σ-σ and that the data are drawn from normal distribu- tions. Use α 0.05 (a) Test the hypothesis and find the P-value (b) Explain how the test could be conducted with a confidence interval. than μ2? be used to obtain B 0.05 if u, is 2.5...
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