Heteroskedasticity occurs when the variance of the errors differs across observations i.e. variances are not constant.

Heteroskedasticity could of be two types:

Heteroskedasticity could of be two types:

**1. Unconditional Heteroskedasticity:**When variance does not systematically increase or decrease with changes in the value of independent variable. It is violation of assumption 4 but does not upholds any serious problems with regression.**2. Conditional Heteroskedasticiy:**It exists when error variance changes with the value of independent variable and it is more problematic.**Consequences of (conditional) Heteroskedasticity:**- It does not affect consistency but it can lead to wrong inferences.
- Coefficient estimates are not affected.
- It causes the F-test for the overall significance to be unreliable.
- It introduces bias into estimators of the standard error of regression coefficients; thus t-tests for the significance of individual regression coefficients are unreliable.
- When Heteroskedasticity results in underestimated standard errors, t-statistics are inflated and probability of Type-1 error increases.
- When Heteroskedasticity results in overestimated standard errors, t-statistics are deflated and probability of Type-2 error increases.

**Testing for Heteroskedasticity:**Heteroskedasticity can be tested by

**Plotting residuals**on a graph and judging a relationship with respect to observations on the x-axis. A more stringent measure is the**Breush-Pagan Test**which involves regressing the squared residuals from the estimated regression equation on the independent variables in the regression.- Null Hypothesis = No conditional Heteroskedasticity exists.
- Alternative Hypothesis = Conditional Heteroskedasticity exists.

**Test statistic**= n x R^{2}_{Residuals}_{}

Critical value can be calculated from chi-square distribution table with degree of freedom = no. of independent variables (k)

If

**test statistic > critical value**reject null hypothesis and conclude that conditional Heteroskedasticity exists in the regression model.

**Correcting for Heteroskedasticity:**

Two different methods can be used to correct Heteroskedasticity.

**1.**Computing

**robust standard errors**corrects the standard errors of the linear regression model's estimated coefficients to deal with conditional heteroskedasticity.

**2.**

**Generalized least squares**(GLS) method is used to modify the original equation in order to eliminate the heteroskedasticity.

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