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Conducing a simple regression and a multiple regression

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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.

Income Sales Competitor
219.17653 708.97231 0
464.24351 1559.5697 0
285.72038 627.96458 1
361.87025 658.56853 1
338.86999 898.42678 1
199.51553 818.22042 0
426.34978 814.61226 1
227.75345 480.48037 1
421.56145 1575.6002 0
355.44418 621.0052 1
418.99875 977.30933 1
294.76422 1041.4825 0
147.13047 372.31767 1
209.49585 794.36815 0
301.38837 997.51438 0
472.72826 1642.8883 0
111.61568 241.0804 1
167.46639 438.00819 1
388.80013 1482.9168 0
134.73727 464.99457 1
495.1347 1072.2251 1
238.62761 467.07217 1
299.41772 952.33309 0
226.2798 679.95184 1
166.52278 560.42405 1
463.21752 1489.9119 0
135.13764 491.83926 0
270.46585 605.95229 1
412.19025 972.99139 1
129.77429 330.35447 1
305.34841 1147.9047 0
206.84525 688.86681 0
476.69868 1179.6488 1
419.81398 960.66892 1
281.17869 690.25882 1
401.31977 890.18406 1
302.55583 1155.52 0
117.35208 682.57403 0
367.71406 1308.5818 0
164.64894 437.73965 1
456.72928 1699.494 0
220.76865 700.17723 0
381.68252 1307.5377 0
117.0497 394.41721 1
231.37886 575.30526 1
294.51741 967.85099 0
122.10885 145.1625 1
336.38976 685.6216 1
306.30786 640.5577 1
398.17839 969.17607 1.

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