You work for a company that has a number of take-out pizza stores located in Illinois. You want to produce a model that predicts sales at a location based on the total income of the surrounding neighborhood. This will be used for choosing new locations. The data set pizzasales.dta gives sales (in thousands of dollars) and local income (in millions of dollars) for 50 different stores. There is also a dummy variable equal to 1 if your main competitor chain also has a store in the neighborhood, and zero otherwise.

(a) Run a regression of sales against local income (only). Based on this regression, give an interval that you are 95% confident will contain your sales in a neighborhood with total income $200M. Do you think this regression is useful for planning your chain's expansion?

(b) Now use the data on your competitor's presence or absence to produce a better model. Your model should take into account the fact that what your competitor takes from you is market share. (i.e., the competitor doesn't just take away a fixed amount of business -- it competes with you for each additional dollar the neighborhood spends on pizza.) Based on your new regression, give intervals that you are 95% confident will contain your sales in a neighborhood with total income $200M, both with and without the presence of a competitor. Are these intervals more useful for planning your expansion?

(c) Suppose you are considering whether or not to start up a store in a particular neighborhood, where your competitor already has a store. The rental price for this location is quite high, so that the break-even figure for sales is $400,000. How high does local income have to be before you can expect to make a profit on average at this location? Use your model from part (b) to answer this question.