This tool accurately estimates feasible generalized least squares parameters for your regression analysis.

## How to Use the FGLS Estimator Calculator

Enter the following data points into the calculator:

**Number of Observations (N):**The total number of observations in your dataset.**Number of Independent Variables (K):**The number of independent variables in your regression model.**Sum of squares of independent variables:**The summation of the squared values of all independent variables in your dataset.**Variance of Dependent Variable (σ²):**The variance of the dependent variable in your regression model.**Sum of squared residuals:**The total sum of the squared differences between the observed and predicted values of your regression model.

Once you have entered all the required data, click the **Calculate** button to compute the FGLS estimator.

## Explanation of the Calculations

The calculator computes the Feasible Generalized Least Squares (FGLS) estimator using the following steps:

- Calculate the estimated variance of the errors, γ̂, using the formula:

γ̂ = Sum of squared residuals / (N – K – 1) - Calculate the standard error of the beta coefficients, β̂, using the formula:

β̂_{se}= sqrt(σ² / (Sum of squares of independent variables * γ̂))

## Limitations

This calculator makes several assumptions that may limit its applicability:

- The residuals are normally distributed.
- The model is correctly specified.
- There is no perfect multicollinearity among the independent variables.

Be sure to validate these assumptions before relying on the results from this calculator for critical decision-making.

## Use Cases for This Calculator

### Calculate FGLS estimator for a single-variable regression

Enter your data points for the independent and dependent variables to quickly calculate the Feasible Generalized Least Squares (FGLS) estimator. This estimation method takes into account heteroscedasticity in the data, providing more reliable coefficient estimates.

### Estimate FGLS for a multi-variable regression model

Input multiple sets of independent variables along with the dependent variable to obtain a comprehensive FGLS estimation for a complex regression model. This tool accounts for variance differences across variables, producing accurate coefficient estimates for each independent variable.

### Improve coefficient accuracy using FGLS method

By utilizing the FGLS estimator, you can significantly enhance the accuracy of the coefficient estimates in your regression analysis. This method adjusts for heteroscedasticity, leading to more precise and reliable regression results.

### Handle heteroscedasticity in regression analysis

When heteroscedasticity is present in your data, traditional least squares methods may provide biased coefficient estimates. FGLS estimation is designed to address this issue, allowing you to account for varying levels of variance in your regression model.

### Assess the impact of outliers on regression results

Outliers can distort regression analysis results, impacting the reliability of coefficient estimates. By applying the FGLS estimator, you can mitigate the influence of outliers and obtain more robust regression coefficients that better represent the data trends.

### Perform robust regression analysis with FGLS

Conduct a robust regression analysis using the FGLS estimator to account for potential model misspecification and heteroscedasticity. This approach provides more accurate parameter estimates, even when data assumptions are not perfectly met.

### Enhance predictive power with FGLS estimation

By incorporating FGLS estimation in your regression models, you can improve the predictive power of your analysis. This method adjusts for heteroscedasticity, leading to more reliable predictions and better model performance.

### Apply FGLS in econometric modeling

When working on econometric models that exhibit heteroscedasticity, FGLS estimation is a valuable tool to ensure the integrity of your regression results. By incorporating FGLS, you can obtain coefficient estimates that accurately reflect the true relationships in the data.

### Compare FGLS results with OLS estimates

Compare the results of FGLS estimation with Ordinary Least Squares (OLS) estimates to observe the impact of heteroscedasticity on regression coefficients. FGLS provides improved estimates in the presence of non-constant variance, offering insights into the robustness of your regression model.

### Quantify uncertainty in coefficient estimates

Use the FGLS estimator to quantify the uncertainty associated with coefficient estimates in your regression analysis. By accounting for varying levels of variance, FGLS provides a more realistic assessment of parameter precision, helping you make informed decisions based on the data.