Math Problem Statement

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

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Statistics
Algebra

Formulas

y = mx + b (Equation of a line)
Slope formula: m = (Σ(x - x̄)(y - ȳ)) / Σ(x - x̄)²
Intercept formula: b = ȳ - m * x̄

Theorems

Least Squares Method

Suitable Grade Level

Grades 10-12