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!