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 + Bilog(nox) + Bzrooms + u. (i) What are the probable signs of B1 and B,? What is the interpretation of B1? Explain. (ii) 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 B,? (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?
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 + Bilog(nox) + Bzrooms + u. (i) What are the probable signs of B1 and B,? What is the interpretation of B1? Explain. (ii) 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 B,? (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?
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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![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 + Bilog(nox) + Bzrooms + u.
(i) What are the probable signs of B1 and B,? What is the interpretation of B1? Explain.
(ii) 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 B,?
(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa7405d0-536a-4f1e-bea9-f49bdb96316d%2F2e56ce2a-0fc8-4532-b6a0-ec079a2ba12b%2Fps9i5we.png&w=3840&q=75)
Transcribed Image Text: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 + Bilog(nox) + Bzrooms + u.
(i) What are the probable signs of B1 and B,? What is the interpretation of B1? Explain.
(ii) 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 B,?
(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?
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