Question

Question 3:

You are analyzing air quality in Californian metropolitan areas and are given following data from 30 areas:

airqual: an indicator of air quality (the lower the better) in the area.

valadd: the aggregate value added of manufacturing companies in the area per year.

rain: amount of rain per year in inches.

coast: Yes if the area is coastal, No else.

density: population density (number of people per square mile).

income: average income per person in the area in US Dollar.

The data is given in the file Q3_Data_2018.xlsx. The variable coastdum below is a dummy variable made from coast (do it yourself).

1. Estimate the following regression by OLS:

airqual=β0+β1valadd+β2rain+β3coastdum+β4density+β5income+e.                 1)

where the βs are unknown coefficients to be estimated, and e is a random error term. Report the results and interpret the coefficients. How much of the variation in airqual is explained by the independent variables?

2. Discuss which assumptions must be fulfilled for OLS to provide unbiased estimates of the coefficients in 1)

3. Based on the results in 1), which variables have a significant effect on air quality?

A research colleague says that the regression in 1) may be plagued by multicollinearity. He suggests that you should exclude the variable income and estimate the following regression by OLS:

airqual=β0+β1valadd+β2rain+β3coastdum+β4density+e.                 2)

4. Interpret the results from 2). Do you agree with your research colleague? Explain why or why not.

Based on the above analyses, what is your conclusion on what affects air quality in Californian metropolitan areas?

Hint

for Y = bo + b1*X1 + b2*X2 + b3*X3 + b4*X4

b1 is the change in Y with one unit increase in X1. similarly for others. assumptions of multi-co-linearity are: 1) normality of residuals (checked from PP plot) 2) homogeneity of error variance (checked from Residual plot) 3) no multi-co-linearity (checked from correlation matrix and VIF)