Using the Census data provided in class, or the CCHS, or your own data, pick a key dummy variable or quantitative variable you are interested in (call it y). Then, pick a dummy variable (e.g., a level of a qualitative variable) you are also interested in (call it y). (a) (5 points) Using the t.test function in R, estimate the difference in average Yi for the two levels of Xi using a model like y x. What are the results of the test? (b) (5 points) Now, using the lm function in R, estimate your model again from (a), and then consider the summary() of your regression model. What is the coefficient on x? (c) (5 points) How do your answers in (a) and (b) compare? Explain why, by relating what we know about CEFs and t-tests. 1For instance, if this is estimates a production function with constant returns to scale. (d) (5 points) Now, add another variables to your model in (b). Does the coefficient on x change? Why or why not? Explain.