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Assignment 4
BECO4003
November 13, 2024
1. The consequences of heteroskedasticity?
2. Please use example1.wf1 on the moodle and run the simple regression, y = β0 + β1x + u.
(a) Can you reject the null hypothesis, H0 : V ar(u|x) = σ
2 against the alternative H1 : V ar(u|x) = σ
2 at the significance level of 5%?
(b) If one would like to test the null hypothesis H0 : β1 = 0 against the alternative hypothesis H1 : β1 = 0, which test should be used?
3. Please use example3.wf1 on the moodle and run the simple regression, y = β0 + β1x + u.
(a) Can you reject the null hypothesis, H0 : V ar(u|x) = σ
2 against the alternative H1 : V ar(u|x) = σ
2 at the significance level of 5%?
(b) If one would like to test the null hypothesis H0 : β1 = 0 against the alternative hypothesis H1 : β1 = 0, which test should be used?
4. Consider the simple regression, y = β0 + β1x + u, u ∼ N(0, 1 + x
2
).
Here, the variance of u is known, and all assumptions except A.5 are satisfied. How should the GLS method be implemented?
5. Please use example4.wf1 on the moodle and run the mutiple regression,
y = β0 + β1x1 + β2x2 + β3x3 + u.
(a) Can you reject the null hypothesis, H0 : V ar(u|x) = σ
2 against the alternative H1 : V ar(u|x) = σ
2 at the significance level of 5%?
(b) Can you reject the null hypothesis, H0 : β1 = β3 against the alternative H1 : β1 − β3 = 0 at the significance level of 5%?
(c) Can you reject the null hypothesis, H0 : β1 = β3 −β2 + 1 = 0 againstthe alternative H1 : β1 = 0 or β3 −β2 + 1 = 0 at the significance level of 5%?
6. When and why should we utilize machine learning techniques such as LASSO?