Question

the annual profits for a company are given in the following table, where x represents the number of years since 2008, 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 2018, rounded to the nearest thousand dollars.

regression equation:

final answer: thousand dollars

Explanation:

Step1: Input data into calculator

Using a statistics calculator, input the \(x\)-values (\(0,1,2,3,4\)) and \(y\)-values (\(165,155,196,219,218\)).

Step2: Find the linear regression equation

The linear regression equation formula is \(y = ax + b\). After calculation, \(a\approx13.6\) and \(b = 154.8\). So the regression equation is \(y=13.6x + 154.8\).

Step3: Find \(x\) for 2018

Since \(x\) represents years since 2008, for 2018, \(x=2018 - 2008=10\).

Step4: Substitute \(x = 10\) into the equation

Substitute \(x = 10\) into \(y=13.6x + 154.8\), we get \(y=13.6\times10+154.8=136 + 154.8=290.8\approx291\).

Answer:

Regression Equation: \(y = 13.6x+154.8\)
Final Answer: \(291\) thousand dollars