Problem Set 2

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University of New South Wales *

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2206

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Statistics

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Apr 3, 2024

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1. (1 point) Imagine that you don’t believe that equation (1) is the correct population regression model. Instead you think that the correct population regression model should take into account that the length of a book affects sales by a different amount depending on if the book was originally written in English and if the book is fiction. Estimate this regression using OLS and interpret all the estimates (you must include a screen-shot of Stata do-file commands estimating the equation). You can assume that all Gauss-Markov assumptions hold when interpreting the estimates (Answer in less than 60 words for each parameter you interpret) The constant can be interpreted as non-fiction, non-English books with 0 pages (length=0) should have sales of 216,314 books. Coefficient of length can be interpreted as one additional page in length sells 993 extra non-fiction, non-English books. Coefficient of fiction can be interpreted as fiction books with no pages (length=0) should sell 184,124 books extra in comparison to non-fiction books with no pages. Coefficient of English can be interpreted as books written in English with no pages should sell 302,346 books extra in comparison to non-English books with no pages. Coefficient of length*fiction can be interpreted as one additional page will affect the sales of fiction books by 579 less than the effect for non-fiction books. Finally, coefficient of length*english can be interpreted as one additional page will affect the sales of English books 26.5 less than the same effect on non-English books. 2. (1 point) Using the estimates from question 1, provide a prediction of how much an English non-fiction book of 200 pages should sell. Sales = 216.31 + 200*0.993 + 302.35 – 200*0.026 = 712.06 books

3. (1 point) Perform a statistical test to determine whether equation (1) suffers from heteroskedasticity . What is the result of this test (use 5% significance level)? (you must include a screen-shot of Stata do-file commands estimating the equation) H 0 : all parameters = 0 H 1 : at least one parameter ≠ 0 Performing a statistical test, the F statistic is 19.01. Hence, we reject the null (at the 5% significance level) which means that equation (1) suffers from heteroskedasticity. 4. (1 point) Assume that V ar(U|length, fiction, english) = σ2×(length/500) where U is the error term of equation (1). Use this information to estimate equation (1) using Weighted Least Squares (in STATA if you need to perform a regression of y on x where you don’t want to include the constant you can write the following: reg y x, nocons) (you must include a screen-shot of Stata do-file commands estimating the equation).

5. (1 point) The book publisher tells you that the length of a book may have been measured with some error. They assure you that while the errors are quite frequent, they are completely at random. Do you expect that α^ 1 you estimated in question 1. to be biased? In which direction you expect the bias to go? (Answer in less than 80 words) Yes, I think as there are still errors in the measurement, α^ 1 will have attenuation bias. Since the estimate α^ 1 is positive, it is expected for the direction of the bias to be negative.

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