# How to correct Heteroscedasticity with Weighted (Generalised) Least Squares in Eviews

To correct heteroskedasticity with Weighted (Generalized) Least Squares (WLS/GLS) in EViews, follow these steps:

### Step-by-Step Guide:

1. Run Initial OLS Regression:
• Go to Quick -> Estimate Equation.
• Enter your regression equation (e.g., Y = C(1) + C(2)*X1 + C(3)*X2).
• Click OK to estimate using Ordinary Least Squares (OLS).
2. Diagnose Heteroskedasticity:
• Check for heteroskedasticity by going to View -> Residual Diagnostics -> Heteroskedasticity Tests.
• Choose and run a test (e.g., Breusch-Pagan-Godfrey, White test).
• If heteroskedasticity is detected, proceed with the next steps.
3. Estimate Weights:
• Obtain the residuals from the initial OLS regression.
• Go to Proc -> Make Residual Series to create a series of residuals.
• Create a new series for the weights. Typically, weights are the inverse of the variance of the residuals. For example, you can generate weights as follows:
• Open the command window and type series weight = 1/@abs(resid).
• This uses the absolute value of residuals to create weights.
4. Run Weighted Least Squares Regression:
• Go to Quick -> Estimate Equation.
• Enter your regression equation again.
• Click on Options before estimating the equation.
• In the Weight field, enter the name of the weight series you created (e.g., weight).
• Click OK to estimate the equation using Weighted Least Squares (WLS).
5. Interpret Results:
• Review the output. The coefficients and their standard errors are now adjusted for heteroskedasticity.
• Check the significance of the variables and interpret the model as usual.

### Detailed Explanation:

• Initial OLS Regression: This provides baseline estimates and residuals, which help in diagnosing heteroskedasticity.
• Diagnose Heteroskedasticity: Tests like Breusch-Pagan or White indicate whether the error variance changes with the level of an independent variable.
• Estimate Weights: Weights help correct for heteroskedasticity by giving less weight to observations with higher variance.
• Weighted Least Squares: WLS adjusts the regression to account for heteroskedasticity, providing more reliable coefficient estimates.

### Example:

Suppose your model is: Y=β0+β1X1+β2X2+ϵY = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon

• Run OLS regression.
• Diagnose heteroskedasticity (e.g., using Breusch-Pagan test).
• Create a weight series based on residuals.
• Re-run the regression with weights.

By using WLS/GLS, you adjust for heteroskedasticity, ensuring more accurate and reliable regression results.

### Practical Implications:

Correcting for heteroskedasticity using WLS ensures that your model’s assumptions hold, leading to more trustworthy inferences and predictions. This technique is particularly useful in empirical research where heteroskedasticity can bias standard OLS estimates.

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