Arnold Tofu owns and operates a chain of 12 vegetable protein "hamburger" restaurants in northern Louisiana. Sales figures and profits for the stores are provided in the table below
Sales are given in millions of dollars; profits are in hundreds of thousands of dollars. Calculate a regression line for the data. What is your forecast of profit for a store with sales of $24 million? $30 million?
Store Profits Sales
1 14 6
2 11 3
3 15 5
4 16 5
5 24 15
6 28 18
7 22 17
8 21 12
9 26 15
10 43 20
11 34 14
12 9 5
Students must recognize that "sales" is the independent variable and "profits" is dependent. Store number is not a variable, and the problem is not a time series. The regression equation is:
y-hat = 5.936 + 1.421x (y-hat = profit, x = sales). A store with $24 million in sales is estimated to produce a profit of 40.04 or $4,004,000. Similarly, $30 million in sales should yield 48.566 or $4,856,600 in profit.
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