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The document contains several tasks, primarily related to calculating the standard deviations and regression for the data set. Here's a breakdown of what is needed:

1. **Calculate the standard deviations for all variables**:
   - You are asked to compute the standard deviation for each variable: **Peso (X₁)**, **Altura (X₂)**, and **Edad (X₃)**. This requires calculating the mean (average) for each column, then using the standard deviation formula:

     \[
     \sigma_X = \sqrt{\frac{\sum_{i=1}^n (X_i - \bar{X})^2}{n}}
     \]

2. **Apply the typical deviation \( S_{1,23} \)**:
   - Using the regression model \( X_1 = 3.65 + 0.855X_2 + 1.506X_3 \), you'll calculate the predicted \( X_1 \) values. The typical deviation (standard error) \( S_{1,23} \) follows the formula given:

     \[
     S_{1,23} = \sqrt{\frac{\sum_{i=1}^{12} (X_1 - X_{i,\text{est}})^2}{N}}
     \]

3. **Estimate the standard error of the population \( \hat{S}_{1,23} \)**:
   - The formula is provided as \( \hat{S}_{1,23} = \sqrt{\frac{N}{N-3}}S_{1,23} \).

4. **Calculate the coefficient of determination \( R_{1,23}^2 \)**:
   - This uses the formula \( R_{1,23}^2 = 1 - \frac{S_{1,23}^2}{S_1^2} \), where \( S_1^2 \) is the variance of \( X_1 \), and \( S_{1,23}^2 \) is the residual variance.

### I can assist in calculating these steps. Shall I start with the standard deviations for each variable? If you want, I can extract the values from the table and go step by step.

Let me know if you have any specific questions or need more details! Here's a set of relative questions based on this information:

1. How would you calculate the mean and variance of a variable like \( X_1 \)?
2. Why is the regression model important in calculating the typical deviation \( S_{1,23} \)?
3. What role does the standard error play in estimating population parameters?
4. How do you interpret the coefficient of determination \( R^2 \)?
5. What happens if the regression model provides a poor fit—how does it affect \( S_{1,23} \)?

**Tip:** Always ensure that you use the correct degrees of freedom when estimating standard deviations or errors, especially in small sample sizes!

Calculate standard deviations and apply regression formulas to estimate and determine statistical values for the given dataset.

Learn how to calculate standard deviations and apply regression formulas to estimate and determine statistical values, including typical deviation and coefficient of determination for a dataset of weight, height, and age.

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