Regression Analysis R² 0.808 Adjusted R² 0.693

Outputregression Analysisr²0808adjusted R²0693n9r0899k3std Error0

Analyze a regression model with an R-squared value of 0.808, an adjusted R-squared of 0.693, and a standard error of 0.221, based on 9 observations. The dependent variable is GDP per Population, with explanatory variables including DJIA, TAX, and LAG_RATE. The ANOVA table indicates the overall model significance, while the coefficients table provides estimates, standard errors, t-values, p-values, confidence intervals, and variance inflation factors (VIF). The Durbin-Watson statistic is 0.99, suggesting potential autocorrelation issues.

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Regression analysis serves as a fundamental statistical technique used to understand the relationship between a dependent variable and one or more independent variables. In this context, the analysis aims to explore how stock market indices (DJIA), taxation policies (TAX), and lagged economic variables (LAG_RATE) influence GDP per capita, which is critical for policymakers and economists concerned with economic growth drivers.

The reported model exhibits an R-squared value of 0.808, indicating that approximately 80.8% of the variability in GDP per capita (GDP_POP) is explained by the model. The adjusted R-squared, which adjusts for the number of predictors relative to observations, is slightly lower at 0.693, suggesting that the model's explanatory power remains substantial but accounts for potential overfitting concerns, given the small sample size of 9 observations.

The standard error of 0.221 reflects the typical deviation of observed values from those predicted by the model. A lower standard error implies more precise predictions. The ANOVA table confirms the overall statistical significance of the regression model, with a significant F-test indicating that the combined explanatory variables predict GDP per capita better than a model with no predictors.

Analyzing individual coefficients, the intercept is estimated at approximately 36.75, although the precise p-value and confidence intervals are not provided. The coefficients for DJIA, TAX, and LAG_RATE are negative, suggesting an inverse relationship with GDP per capita; specifically, increases in stock market indices, taxation, or lagged rates tend to correlate with decreases in GDP per capita, holding other factors constant. However, the p-values associated with these coefficients exceed the conventional significance threshold (p > 0.05), indicating that these relationships may not be statistically significant within this small sample.

The variance inflation factors (VIFs) for the predictors are not explicitly listed but are crucial for diagnosing multicollinearity. High VIFs would suggest that the independent variables are highly correlated, which can inflate standard errors and undermine the reliability of coefficient estimates. The reported Durbin-Watson statistic of 0.99 indicates potential autocorrelation in residuals, which biases standard errors and can lead to misleading inferences.

Given the small sample size and potential issues such as multicollinearity and autocorrelation, caution must be exercised when interpreting the model's results. The model’s predictive capacity appears substantial, but the insignificance of individual predictors and residual diagnostics raises questions about its robustness. Future research should incorporate larger datasets, alternative variables, and diagnostic testing to validate these findings.

In conclusion, while the regression model provides insights into factors influencing GDP per capita, limitations related to sample size, autocorrelation, and predictor significance suggest that these findings are provisional. Policymakers should consider these factors in conjunction with broader economic analyses before making decisions primarily based on this model.

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