Question

the annual profits for a company are given in the following table, where x represents the number of years since 1997, and y represents the profit in thousands of dollars. write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. using this equation, find the projected profit (in thousands of dollars) for 2006, rounded to the nearest thousand dollars.
years since 1997 (x) 0 1 2 3 4
profits (y) (in thousands of dollars) 131 168 202 193 221

Explanation:

Step1: Enter data into calculator

Enter \(x = 0,1,2,3,4\) and \(y = 131,168,202,193,221\) into a statistics calculator.

Step2: Find linear regression equation

Using the calculator, the linear regression equation is \(y=20.4x + 130.8\).

Step3: Calculate \(x\) for 2006

Since \(x\) is years since 1997, for 2006, \(x = 2006 - 1997=9\).

Step4: Substitute \(x = 9\) into the equation

\(y=20.4\times9 + 130.8\).

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Answer:

The projected profit for 2006 is \(314.4\) thousand dollars.