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The question is asking about the behavior of the coefficient of determination, also known as **R²**, in the context of a classical multiple linear regression model.

The coefficient of determination (R²) measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating no explanatory power.

Here are the options:

1. **Aumenta siempre que se incorpora una nueva variable explicativa.**
   - R² always increases when a new explanatory variable is added, regardless of whether the variable is significant or not.

2. **Disminuye siempre que se añade una variable explicativa significativa.**
   - R² decreases every time a significant explanatory variable is added. 
   - This statement is incorrect since R² generally does not decrease with the addition of variables.

3. **Aumenta si la variable que se incorpora tiene un valor estadístico t mayor que 3.**
   - R² increases if the new variable has a t-statistic greater than 3. 
   - While a high t-statistic indicates significance, the statement is too specific and doesn't fully capture the general behavior of R².

4. **Disminuye siempre que se añade una variable explicativa adicional.**
   - R² decreases every time an additional explanatory variable is added. 
   - This is incorrect because R² does not decrease when adding variables.

The **correct answer** is:
- **Aumenta siempre que se incorpora una nueva variable explicativa.**
   - This is because R² either stays the same or increases when new explanatory variables are added. However, adding variables indiscriminately can lead to overfitting, and that's why adjusted R² is often used to penalize unnecessary complexity.

Would you like a more detailed explanation of R² or its adjusted version?

Here are five related questions for further understanding:
1. What is the difference between R² and adjusted R²?
2. How does adding irrelevant variables affect the adjusted R²?
3. What is multicollinearity, and how does it affect regression models?
4. How is the t-statistic used to determine the significance of a variable in a regression model?
5. Why is overfitting a concern in multiple linear regression models?

**Tip**: Always check the adjusted R² in regression models, as it accounts for the number of variables, helping to avoid overfitting.

¿Cuál es el coeficiente de determinación en un modelo de regresión lineal múltiple clásico?

Understand the behavior of the coefficient of determination (R²) in a classical multiple linear regression model. Explore how R² changes when new explanatory variables are added and why it does not decrease in this context.

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