Question: [23 points] Suppose a researcher, using more than 2000 datasets on BMI and urban or rural status of individuals estimates the OLS regression, where Rural=1 if the person lives in a Rural location and =0 if the person lives in Urban location. As BM I increases, the person is relatively more obese.

1. [4 pts] What are the average BM I of individuals residing in urban and rural location, respectively, show you work?
2. [4 pts] What is R2 described? Then interpret the true meaning of R2 in this regression.

c) [3 pts] explain, in detail, the true meaning of b1 (coefficient of Rural) in the regression.

d) [3 pts] Construct a 95% confidence interval for the difference in BM I between urban and rural residents.

e) [4 pts] Test the null hypothesis that the difference in BM I between urban and rural residents is from zero, against the alternative that it is not, at the 99 % level of significance. Show all your work and what is your conclusion?

f) [5 pts] If I suspect that heteroskedasticity is present in the model .i.e., we don’t believe that the variance of people’s BMI in urban location would be the same as the variance of people’s BMI in rural location , what am I suspecting to be true (i.e. define heteroskedasticity) ? What OLS assumption is violated if this were true? What are the repercussions regarding my analysis if I do not correct for this problem?

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