The annual profits for a company are given in the following table, where x represents the number of years since 2002, 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 hundredth*. Using this equation, find the projected profit (in thousands of dollars) for 2010, rounded *to the nearest thousand dollars*.

Years since 2002 (x)Profits (y)
(in thousands of dollars)

00

135135

11

160160

22

157157

33

192192

44

1925  227


To solve this, we need to calculate the linear regression equation in the form:

\[
y = mx + b
\]

Where:
- \( y \) is the profit in thousands of dollars,
- \( x \) is the number of years since 2002,
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept.

### Step 1: Gather the data

The data provided is:

\[
\begin{array}{|c|c|}
\hline
\text{Years since 2002 (x)} & \text{Profits (y) in thousands of dollars} \\
\hline
0 & 0 \\
1 & 135 \\
2 & 160 \\
3 & 157 \\
4 & 192 \\
5 & 227 \\
\hline
\end{array}
\]

### Step 2: Calculate the slope (\(m\)) and intercept (\(b\))

We will apply the formulas for slope and intercept again. Let me calculate those for you.

The annual profits for a company are given in the following table, where x represents the number of years since 2002, 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 hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2010, rounded to the nearest thousand dollars.

Learn how to find the linear regression equation for company profits since 2002. This problem uses statistical concepts like slope and y-intercept to predict future profits, rounded to the nearest thousand dollars. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation