Math Problem Statement

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Find the least squares regression line of mass on height.

Solution

The least squares regression line of mass yy (in kg) on height xx (in cm) is given by the equation:

y=0.682x50.750y = 0.682x - 50.750

This equation describes how mass relates to height, with a slope of approximately 0.6820.682 kg per cm, and an intercept of approximately 50.750-50.750 kg.

Would you like a breakdown of these steps or further clarifications?

Here are some related questions:

  1. How can we interpret the slope of the regression line?
  2. How is the y-intercept meaningful in this context?
  3. How would we calculate predicted mass for a height of 160 cm using this regression line?
  4. What is the significance of residuals in regression analysis?
  5. How do we assess the accuracy of this regression model?

Tip: The slope tells you how much the mass is expected to increase per unit increase in height.

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Least Squares Method

Formulas

y = mx + c (equation of a straight line)
m = Σ(x - x̄)(y - ȳ) / Σ(x - x̄)² (slope formula)
c = ȳ - m * x̄ (intercept formula)

Theorems

Least Squares Theorem

Suitable Grade Level

Grade 10-12