1. Let y = Px + u, i = 1, ..., n, where Assumptions 1-5 of...
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1. Let y₁ = P₁x + u¡, i = 1, ..., n, where Assumptions 1-5 of the simple linear regression model are satisfied. Define B₁ = ₁+yn x1+xn Explain whether ₁ is consistent or not in this setup. (2 marks) 2. For the same model as above, show that the variance of B₁ is larger than the variance of ₁, where B₁ denotes the OLS estimator. Please refrain from referring to the Gauss-Markov theorem as part of your answer. (4 marks) 3. Consider the following estimated regression model: outphr, 431.259.264wkhoursi, where outphr; denotes output per hour for worker i, i = 1, ..., n, and wkhours; denotes weekly working hours. = = Let Ê (outphr) = 82.92, var(outphr;) = 307.45, Ê(wkhours;) = 37.6 and var(wkhours;) : 3.217, where Ê (.) denotes the sample average and var (.) denotes the sample variance. Find the expected weekly output of a typical worker, i.e. estimate E (outphr; × wkhours;). (4 marks) 1. Let y₁ = P₁x + u¡, i = 1, ..., n, where Assumptions 1-5 of the simple linear regression model are satisfied. Define B₁ = ₁+yn x1+xn Explain whether ₁ is consistent or not in this setup. (2 marks) 2. For the same model as above, show that the variance of B₁ is larger than the variance of ₁, where B₁ denotes the OLS estimator. Please refrain from referring to the Gauss-Markov theorem as part of your answer. (4 marks) 3. Consider the following estimated regression model: outphr, 431.259.264wkhoursi, where outphr; denotes output per hour for worker i, i = 1, ..., n, and wkhours; denotes weekly working hours. = = Let Ê (outphr) = 82.92, var(outphr;) = 307.45, Ê(wkhours;) = 37.6 and var(wkhours;) : 3.217, where Ê (.) denotes the sample average and var (.) denotes the sample variance. Find the expected weekly output of a typical worker, i.e. estimate E (outphr; × wkhours;). (4 marks)
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1 The first question asks to explain whether the estimator 1 is consistent or not in the given setup where 1 is defined as the sum of the last observa... View the full answer
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Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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