The following equation describes the median housing price in a community in term

Question

  The following equation describes the median housing price in a community in terms of

amount of pollution (nox for nitrous oxide) and the average number of rooms in houses in

the community (rooms):

log(price) = B0 + B1 * log (nox) + B2 *rooms + u

(i)   What are the probable signs of b1  and b2 ? 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 up-

ward or a downward biased estimator of b1 ?

Explanation / Answer

i) Probabable sign of b1 is negative and probable sign of b2 will be positive.As

b1 = % change in price of house / % change in amount of pollution(due to nox) and

b2 = % change in price odf house / change in average number of rooms in houses in community

This is because as b1 represents price of house sensitive to pollution.So if pollution increases , price of house decreases, due to many people not willing to buy house. Similarly as b2 is coefficient of rooms. So if average number of rooms in house increases, then price of house increases.

Interpretation :So Interpretation of b1 is how much % change in price of house will be there for 1% change in number of rooms.This represents sensitivity of house price to pollution.

ii) nox ( log(nox) and rooms will be neagatively correlated as there will be inverse relation exists between amount of pollution and average number of rooms ,because as many rich people will not buy houses in community if there is more pollution. So Due to this house builders will make only less rooms in house.Hence if pollution is more, there will be less number of rooms in housess on average. So there will be negative correlation between log nox and rooms.

As there is negative correlation between log nox and rooms ,simple regression of log(price) on log(nox) produce an downward biased estimator of b1

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