Question

2. You wish to investigate how local crime rates impact housing prices. You have access to a data set of 506 home sales. This data set contains information on the selling price for a home (price) and the local crime rate (crime) reported in terms of crimes committed per capita per year. You choose to regress the (natural) log of price (lprice log(price)) on crime in Stata and obtain the following results: Source MS 506 194.30 0.0000 0.2783 Adj R-squared0.2768 34803 d f Number of obs F (1, 504) Model Residual 23.5350604 61.0471645 1 23.5350604 Prob F 504 .121125326 R-squared Total 84.582225 505 .167489554 Root MSE lprice Coef. Std. Err. [95% Conf. Interval] -.0251308 10.03182 crime .0018029-13.94 0.000 .0167861 597.63 0.000 .0286729.0215887 10.0648 -cons 9.998839

(a) Write down the population regression model, being as specific as possible. (5 points)

(b) What is the meaning of the error term u in this regression? Provide an example of what u represents. (5 points)

(c) What are the estimates of the intercept and slope parameters? Interpret what these estimates mean, being as specific as possible. (15 points)

(d) Why might the estimate of the slope from the simple linear regression above be a biased estimate of the true causal effect of crime rates on housing prices? Be as specific as possible and provide an example in terms of this particular regression. (8 points)

please answer and explain :)))))))))))

Answer 1

1. Population regression model: lprice = β0 + β1*crime + u, where u is the error term.
2. The error term includes the effect of variables that are left out from the regression because of unavailabity of data or suitable proxy variables, it also account for wrong functional form.
3. The intercept tells that the mean house price is e^10.03 when the crime rate is zero. The slope parameter tells us that if the crime rate increases by 1 percent housing price on average decreases by 0.25 percent.
4. The slope from simple linear regression will provide a biased estimate because the housing price are not only affected by crime rates but by many other variables such as pollution level in the locality, access to safe drinking water and connectivity to highways. Thus by omitting variables other than crime rate will lead to omitted variable bias and the estimate will also be biased.