1. (11 Points) Consider the multiplicative model
Yi = 1Xi 2e”i, i=1,…,n
Hint: You can use R for the computations below, but you need to write down your answers in the written part of the exam.
(a) (1 P.) Written answer:
Apply an ln()-transformation to derive the standard simple linear regression model.
(b) (4 P.) Written answers:
Suppose that the following data are observed:
Compute the value of the OLS-estimate ˆ = (X ̃ 0X ̃ ) 1X ̃ 0Y ̃ . Additionally, write down the values of the following quantities:
(X ̃ 0X ̃ ), (X ̃ 0X ̃ ) 1 and X ̃ 0Y ̃ .
(c) (2 P.) Written answers:
Compute the t-test statistic to test (significance level ↵ = 0.05)
H0 : 2 =0 against H1 : 2 6=0 What’s the p-value and what’s your test-decision?
(d) (4 P.) Written answers:
Consider the multiplicative model and show that the elasticity of f(x) = E(Y|X = x) with respect to x equals 2. Comment on the role of the independence between “i and Xi in your derivations.
Assumptions 1-4 of Chapter 3 of our script are assumed to hold for this model. Additionally, i.i.d. 2
you can assume homoscedastic, spherical errors with “i ⇠ N(0, ), and independence between “i and Xi for all i = 1,…,n.
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X ̃i =ln(Xi)
Programming
[SOLVED] CS代考计算机代写 1. (11 Points) Consider the multiplicative model
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