Econometrics in R

Econometrics in R

1. (60) Use the Boston dataset in the MASS package in R to answer the following ques- tions. You may type ?Boston in R to get complete definitions of the variables. The following model describes the median housing price (medv) across communities in the metro Boston area in terms of the amount of pollution (nox for nitrous oxide concentration) and the average number of rooms in a house in the community (rm):

log(medv) = β0 + β1 log(nox) + β2rm + ε. (3)

(a) What are the expected signs of β1 and β2 in this model?

(b) What is the interpretation of β1?

(c) What is the interpretation of β2?

(d) Estimate this model and report your coefficient estimates for the three param- eters in this model along with R2 and the corresponding standard errors.

(e) Interpret R2.

(f) Are you concerned that collinearity is present in this setting?

(g) Why would nox and rooms be negatively correlated?

(h) Would estimating your model of housing prices omitting rooms yield an upward or downward bias in βˆ1 if rooms and nox were negatively correlated, why?

(i) Estimate your model excluding rooms and report your coefficient estimates for the two parameters along with R2 and the corresponding standard errors.

(j) Is your estimate of β1 in the univariate model closer to the truth than in the multiple regressor model you estimated earlier?

(k) What do you make of the vast decrease in R2 when you estimate the univariate model?

(l) Is it possible to include rm2 in model (3)? If yes, why is it useful?

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