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The table and question provided pertain to the results of a multiple linear regression model (RLM) with two explanatory variables \(X_1\) and \(X_2\). Let's break down the information from the image:

### Regression Statistics:
1. **Multiple correlation coefficient (R)**: 0.98
2. **Coefficient of determination (\( R^2 \))**: 0.96 (indicating 96% of the variation in the dependent variable is explained by the model).
3. **Adjusted \( R^2 \)**: 0.95 (takes into account the number of predictors relative to the number of observations).
4. **Standard error (Error típico)**: 0.17
5. **Observations**: 20
6. **F-statistic**: 205.54 (used to evaluate the overall significance of the regression model).

### Coefficients (BETAS) and their statistics:
- **\( \beta_0 \)** (Intercept): 
  - Coefficient: 0.09 
  - Standard error: 0.09
  - T-statistic: 1.03 
  - P-value: 0.32 (not statistically significant)
  - 95% confidence interval: [-0.10, 0.28]
  
- **\( \beta_1 \)** (Coefficient for \( X_1 \)): 
  - Coefficient: 0.50
  - Standard error: 0.14
  - T-statistic: 3.47
  - P-value: 0.00 (statistically significant)
  - 95% confidence interval: [0.20, 0.81]

- **\( \beta_2 \)** (Coefficient for \( X_2 \)): 
  - Coefficient: 0.99
  - Standard error: 0.69
  - T-statistic: 1.45 
  - P-value: 0.17 (not statistically significant)
  - 95% confidence interval: [-0.45, 2.44]

### Interpretation of the dataThe table and question provided pertain to the results of a multiple linear regression model (RLM) with two explanatory variables \(X_1\) and \(X_2\). Let's break down the information from the image:

### Regression Statistics:
1. **Multiple correlation coefficient (R)**: 0.98
2. **Coefficient of determination (\( R^2 \))**: 0.96 (indicating 96% of the variation in the dependent variable is explained by the model).
3. **Adjusted \( R^2 \)**: 0.95 (takes into account the number of predictors relative to the number of observations).
4. **Standard error (Error típico)**: 0.17
5. **Observations**: 20
6. **F-statistic**: 205.54 (used to evaluate the overall significance of the regression model).

### Coefficients (BETAS) and their statistics:
- **\( \beta_0 \)** (Intercept): 
  - Coefficient: 0.09 
  - Standard error: 0.09
  - T-statistic: 1.03 
  - P-value: 0.32 (not statistically significant)
  - 95% confidence interval: [-0.10, 0.28]
  
- **\( \beta_1 \)** (Coefficient for \( X_1 \)): 
  - Coefficient: 0.50
  - Standard error: 0.14
  - T-statistic: 3.47
  - P-value: 0.00 (statistically significant)
  - 95% confidence interval: [0.20, 0.81]

- **\( \beta_2 \)** (Coefficient for \( X_2 \)): 
  - Coefficient: 0.99
  - Standard error: 0.69
  - T-statistic: 1.45 
  - P-value: 0.17 (not statistically significant)
  - 95% confidence interval: [-0.45, 2.44]

### Interpretation of the 
- **High \( R^2 \) (0.96)** indicates that the model explains a large portion of the variability in the dependent variable.
- The **F-statistic (205.54)** is high, indicating the model is statistically significant overall.
- **\( \beta_1 \)** is significant with a p-value of 0.00, meaning \( X_1 \) contributes meaningfully to the model.
- \( \beta_0 \) and \( \beta_2 \) are not statistically significant (p-values > 0.05), meaning their contributions may not be as strong.

### Question:
The question asks what can be inferred from the results obtained, and there are several options:

1. **\( R^2 \) is high, but Fisher's test may be low for 20 observations.**
2. **\( R^2 \) is low considering 20 observations, but Fisher is high.**
3. **The \( R^2 \) is equal to the adjusted \( R^2 \) due to a single significant variable.**
4. **The Fisher index is not a function of \( R^2 \).**

### Best Answer:
- The most suitable answer is likely **Option 3**, which highlights that the \( R^2 \) and adjusted \( R^2 \) are very close, and this could be because of the significance of just one variable (\( X_1 \)) in the model.

Would you like further explanation on any part of this analysis?

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Here are five related questions:
1. How does the F-statistic evaluate the overall significance of the regression model?
2. What is the difference between \( R^2 \) and adjusted \( R^2 \)?
3. Why is it important to check the p-value when interpreting regression coefficients?
4. How would increasing the sample size affect the standard error and confidence intervals?
5. Why might one variable in a multiple regression be significant while another is not?

**Tip**: When evaluating regression models, always check both the significance of individual coefficients (p-values) and the overall fit of the model (\( R^2 \), F-statistic).

¿Qué se puede inferir a partir de los datos obtenidos en un modelo de regresión lineal múltiple (RLM) con dos variables explicativas, X1 y X2?

This page provides an analysis of a multiple linear regression model (RLM) with two explanatory variables (X1 and X2). It includes key statistical metrics such as the coefficient of determination (R² = 0.96), adjusted R², p-values, and F-statistic. The analysis highlights the significance of X1 and interprets the overall fit of the model.

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