Math Problem Statement

Based on the data shown below, calculate the regression line (each value to at least two decimal places): x: [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], y: [12.84, 16.16, 14.58, 17, 16.72, 20.64, 19.36, 22.18, 19.5, 22.22, 20.94, 23.56, 22.58]

Solution

The equation of the regression line based on the given data is:

y=0.79x+12.78y = 0.79x + 12.78

This means the slope of the line is approximately 0.790.79, and the y-intercept is approximately 12.7812.78.

Would you like more details or further explanation on how the regression was calculated?

Here are 5 related questions for further understanding:

  1. How is the slope of a regression line interpreted in practical terms?
  2. What does the y-intercept represent in this context?
  3. What is the meaning of the R2R^2 value in regression analysis?
  4. How would the regression line change if more data points were added?
  5. How can you predict new values using this regression equation?

Tip: When interpreting the slope, think of it as how much the dependent variable (y) changes for each one-unit increase in the independent variable (x).

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Math Problem Analysis

Mathematical Concepts

Algebra
Statistics
Linear Regression

Formulas

y = mx + b
Slope (m) = Σ[(x - x̄)(y - ȳ)] / Σ(x - x̄)^2
y-intercept (b) = ȳ - m * x̄

Theorems

Least Squares Regression Line

Suitable Grade Level

Grades 10-12