Math Problem Statement

Calculate the standard deviations for all involved variables, then apply regression and estimate errors using the given formulas.

Solution

Let's break down and solve the problem step-by-step:

1. Calcular las desviaciones estándar de las variables: Peso (X₁), Altura (X₂), Edad (X₃).

The formula for the standard deviation is:

σ=1n∑i=1n(Xi−Xˉ)2\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} \left( X_i - \bar{X} \right)^2}

We will need:

  • The mean of each variable: X1ˉ,X2ˉ,X3ˉ\bar{X_1}, \bar{X_2}, \bar{X_3}
  • The sum of squared deviations for each.

Data summary:

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Math Problem Analysis

Mathematical Concepts

Standard Deviation
Regression Analysis
Estimation of Error
Coefficient of Determination

Formulas

Standard Deviation Formula: σ = √(1/n Σ(Xi - X̄)^2)
Regression Formula: X1 = 3.65 + 0.855X2 + 1.506X3
Error Estimate: Ŝ_1,23 = √(N/(N - 3) S_1,23)
Coefficient of Determination: R_1,23² = 1 - (S_1,23² / S_1²)

Theorems

Regression and Least Squares Theorem
Standard Deviation and Variance Relationship

Suitable Grade Level

Grades 11-12

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