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) profits (y) (in thousands of dollars)
0 131
1 168
2 202
3 193
4 221

copy values for calculator
open statistics calculator

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (\(0,1,2,3,4\)) and \(y\) - values (\(131,168,202,193,221\)) into a statistics calculator.

Step2: Find the linear regression equation

Using the linear regression function on the calculator, we get the equation \(y = 16.7x+138.8\) (rounded to the nearest tenth).

Step3: Determine the \(x\) - value for 2006

Since \(x\) represents the number of years since 1997, for 2006, \(x=2006 - 1997=9\).

Step4: Calculate the projected profit

Substitute \(x = 9\) into the equation \(y=16.7x + 138.8\).

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Answer:

The linear regression equation is \(y = 16.7x+138.8\). The projected profit for 2006 is \(289\) (in thousands of dollars).