Concepts
Interpret the regression equation that you calculated in the prior section. What is the meaning of y = 6.80+0.62x?
Many people have expressed concern that more and more of our food is grown on massive, factory-style corporate farms and that U.S. agricultural subsidies are contributing to this trend.
Suppose that I had data on farm subsidies and farm size. I regress farm size (measured by gross sales in dollars) on subsidy payments received in the calendar year. I find that a farm with 10 cents more in subsidies has on average 4 cents more in sales.
a) State carefully the ceteris paribus assumption in this case. Do you think this simple regression of Y on X satisfies that assumption? Why or why not? What are some of the other factors that explain our incomes, and do you think these might vary as parental income varies across different families? Explain.
b) Pick one of the "other factors" mentioned in (a). Let's call it x2. Suppose you augmented the simple regression with x2. How do you think this would affect the estimate of the coefficient on farm subsidies received (β1)?
c) Imagine an experiment where a randomly selected group of farms are given a 10% increase in subsidy. In this case, would it matter whether x2 was included in the regression? Explain.