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### Question 1
**a. Comment on the statistical significance or otherwise of the regressors. (3 marks)**

To determine the statistical significance of the regressors, we look at the p-values provided in the regression tables. The typical threshold for significance is 0.05.

From **Table 1**:
- \( C \): p-value = 0.0000 (Significant)
- \( PGNP \): p-value = 0.0065 (Significant)
- \( FLR \): p-value = 0.0000 (Significant)

From **Table 2**:
- \( C \): p-value = 0.0000 (Significant)
- \( PGNP \): p-value = 0.0047 (Significant)
- \( FLR \): p-value = 0.0000 (Significant)
- \( TFR \): p-value = 0.0032 (Significant)

All the regressors in both tables are statistically significant because their p-values are less than 0.05.

**b. Would you say the model fits and why? (2 marks)**

The model fit can be assessed by the \( R^2 \) and Adjusted \( R^2 \) values.

- **Table 1:** \( R^2 = 0.7077 \), Adjusted \( R^2 = 0.6981 \)
- **Table 2:** \( R^2 = 0.7474 \), Adjusted \( R^2 = 0.7347 \)

Since both \( R^2 \) and Adjusted \( R^2 \) are relatively high, it suggests that a significant portion of the variance in the dependent variable \( CM \) is explained by the regressors. Hence, the model fits well.

**c. Compare these regression results in both Tables. What changes do you see? How do you account for them? (5 marks)**

- **Changes:**
  - The constant term \( C \) decreased from 263.6416 to 168.3067.
  - The coefficient for \( PGNP \) slightly changed from -0.0056 to -0.005511.
  - The coefficient for \( FLR \) changed from -2.2316 to -1.768029.
  - The new variable \( TFR \) was added with a coefficient of 12.286864.
  - The \( R^2 \) increased from 0.7077 to 0.7474, and the Adjusted \( R^2 \) also increased.

- **Explanation:**
  - Adding \( TFR \) improves the model fit as indicated by the increase in \( R^2 \) and Adjusted \( R^2 \).
  - The changes in the coefficients suggest that the inclusion of \( TFR \) captures some of the variance that was previously attributed to \( FLR \) and \( PGNP \), leading to a better representation of the relationship between the variables and the dependent variable \( CM \).

**d. Why is it worth adding the variable, TFR, to the model? (5 marks)**

Adding \( TFR \) is justified because:
- The p-value for \( TFR \) is 0.0032, indicating it is statistically significant.
- The \( R^2 \) and Adjusted \( R^2 \) values increased after adding \( TFR \), which means that the model explains more of the variance in the dependent variable \( CM \).
- Including \( TFR \) might better represent the theoretical relationship between the variables and provide a more accurate model.

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Would you like to proceed with more questions or details from the document? Feel free to ask if you have any specific question or topic you'd like to explore further. Here are five related questions you might find helpful:

1. How does the Durbin-Watson statistic help in diagnosing autocorrelation in a regression model?
2. What is the significance of the F-statistic in regression analysis?
3. How do you interpret the confidence intervals in the regression output?
4. What are the implications of multicollinearity in regression analysis?
5. How can you test for heteroscedasticity in a regression model?

**Tip:** Always check the residuals of your regression model for patterns to ensure that your model is the best fit.

Explore the statistical significance of regressors and model fit in regression analysis. Learn how to interpret regression coefficients and assess model adequacy using R^2 and Adjusted R^2 values. Suitable for university-level students and professionals.

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