Question

PLEASE HELPThe annual profits for a company are given in the following table, where x representsthe number of years since 2014, and y represents the profit in thousands of dollars.Write the linear regression equation that represents this set of data, rounding allcoefficients to the nearest hundredth. Using this equation, estimate the calendar yearin which the profits would reach 404 thousand dollars.

Answer 1

The regression model of profit versus year since 2014 gives us the following equation:

$y=31.571x+119.57$

We have to estimate in which year the profits is expected to be 404 thousand dollars.

We can do it by replacing y with 404 and solve for x:

$\begin{gathered} y=404=31.571x+119.57 \\ 31.571x=404-119.57 \\ 31.571x=284.43 \\ x=\frac{284.43}{31.571} \\ x=9 \end{gathered}$

As x represents the number of years since 2014, the calendar year is 2014+9 = 2023.

Answer:

Equation: y=31.571x+119.57

Year: 2023