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
To solve this, we need to calculate the linear regression equation in the form:
Where:
- is the profit in thousands of dollars,
- is the number of years since 2002,
- is the slope of the line, and
- is the y-intercept.
Step 1: Gather the data
The data provided is:
\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.Ask a new question for Free
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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