Math Linear Regression

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 2005, rounded to the nearest thousand dollars.

Years since 1997 (x) Profits (y) (in thousands of 0,1,2,3,4,5. dollars) 81,82,98,107,139,137

Answer 1

This is not an Alegbra I question.

You would not be able to write a linear equation for this set of data since the slope is clearly not constant (notice how x is increasing by increments of 1, but y is increasing by 1, then 16, then 9, then 22, then decreasing by 2). What you can do is plot the points and then draw an approximate best fit line. Once you've drawn the best fit line (to the best of your ability), you can take two points on that line (which will be different than the points you have been given in the prompt) and use those to calculate the slope of the best fit line. Using the slope and one of the two selected points, you can write an equation for the best fit line. After that, you can plug in the x value that represents the year 2005 (how many years is 2005 since 1997?) to find the y-value, which represents the expected profit for that year.