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Arnold Tofu owns and operates a chain of 12 vegetable protein "hamburger" restaurants...

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sta112 | Teacher | Salutatorian

Posted October 4, 2013 at 2:28 AM via web

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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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted October 21, 2013 at 4:30 AM (Answer #1)

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The table provides the sales of the company and the corresponding profit for twelve different stores. To predict the profit earned if the sales are given, using the given information, it is essential to determine the regression line. If the information is plotted on a graph with each point representing sales and the corresponding profit, the regression line is one that nearly passes through each of the points. The error is minimized using statistical tools.

The regression line for the given information can be determined using a software like Excel. The result for the given information is shown in the figure accompanying this response.

From the regression line, if y represents the profit made and x represents the sales, the relation between the two is y = 1.42053*x + 5.93568

For sales of 24 million, the profit made is approximately 40 million and if the sales are 30 million, the corresponding profit is 48.5 million

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