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What are the probable signs of B, and B₂? What is the interpretation of A Why might nox [or more precisely, log(nox)] and rooms be negatively c case, does the simple regression of log(price) on log(nox) produce an up biased estimator of B₁? (iii) Using the data in HPRICE2, the following equations were estimated: (i) (ii)

What are the probable signs of B, and B₂? What is the interpretation of A Why might nox [or more precisely, log(nox)] and rooms be negatively c case, does the simple regression of log(price) on log(nox) produce an up biased estimator of B₁? (iii) Using the data in HPRICE2, the following equations were estimated: (i) (ii)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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whose workers have less than average ability, so that avgtrain and avgabil are negatively correlated, what is the likely bias in B, obtained from the simple regression of avgprod on avgtrain? 9 The following equation describes the median housing price in a community in terms of amount of pol- lution (nox for nitrous oxide) and the average number of rooms in houses in the community (rooms): log(price) = Bo + Blog(nox) + B₂rooms + u. (i) (ii) What are the probable signs of B, and B₂? What is the interpretation of B₁? Explain. Why might nox [or more precisely, log(nox)] and rooms be negatively correlated? If this is the case, does the simple regression of log(price) on log(nox) produce an upward or a downward biased estimator of B₁? (iii) Using the data in HPRICE2, the following equations were estimated: log(price) = 11.71 1.043 log(nox), n = 506, R² = .264. log(price) = 9.23.718 log(nox) + .306 rooms, n = 506, R² = .514. Is the relationship between the simple and multiple regression estimates of the elasticity of price with respect to nox what you would have predicted, given your answer in part (ii)? Does this mean that -.718 is definitely closer to the true elasticity than - -1.043? - 10 Suppose that you are interested in estimating the ceteris paribus relationship between y and X1. For this purpose, you can collect data on two control variables, x₂ and x3. (For concreteness, you might think of y as final exam score, x, as class attendance, x₂ as GPA up through the previous semester, and x, as SAT or ACT score.) Let B, be the simple regression estimate from y on x, and let B, be the multiple regression estimate from y on x₁, x2, X3. (i) If x, is highly correlated with x2 and x3 in the sample, and x₂ and x3 have large partial effects on y, would you expect B₁ and ₁ to be similar or very different? Explain. with and x₂. but
Transcribed Image Text:whose workers have less than average ability, so that avgtrain and avgabil are negatively correlated, what is the likely bias in B, obtained from the simple regression of avgprod on avgtrain? 9 The following equation describes the median housing price in a community in terms of amount of pol- lution (nox for nitrous oxide) and the average number of rooms in houses in the community (rooms): log(price) = Bo + Blog(nox) + B₂rooms + u. (i) (ii) What are the probable signs of B, and B₂? What is the interpretation of B₁? Explain. Why might nox [or more precisely, log(nox)] and rooms be negatively correlated? If this is the case, does the simple regression of log(price) on log(nox) produce an upward or a downward biased estimator of B₁? (iii) Using the data in HPRICE2, the following equations were estimated: log(price) = 11.71 1.043 log(nox), n = 506, R² = .264. log(price) = 9.23.718 log(nox) + .306 rooms, n = 506, R² = .514. Is the relationship between the simple and multiple regression estimates of the elasticity of price with respect to nox what you would have predicted, given your answer in part (ii)? Does this mean that -.718 is definitely closer to the true elasticity than - -1.043? - 10 Suppose that you are interested in estimating the ceteris paribus relationship between y and X1. For this purpose, you can collect data on two control variables, x₂ and x3. (For concreteness, you might think of y as final exam score, x, as class attendance, x₂ as GPA up through the previous semester, and x, as SAT or ACT score.) Let B, be the simple regression estimate from y on x, and let B, be the multiple regression estimate from y on x₁, x2, X3. (i) If x, is highly correlated with x2 and x3 in the sample, and x₂ and x3 have large partial effects on y, would you expect B₁ and ₁ to be similar or very different? Explain. with and x₂. but
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