The least squares method requires that the variance $\sigma _ { z } ^ { 2 }$ of the error variable $\varepsilon$ is a constant no matter what the value of x is.When this requirement is violated,the condition is called:
A) heteroscedasticity.
B) homoscedasticity.
C) influential observation.
D) non-independence of $\varepsilon$.

Question

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Heteroscedasticity is the condition in which the variance of the error variable is not constant for all values of x. This violates the assumption of the least squares method that the variance of the error term should be constant (homoscedastic) for all values of x. When heteroscedasticity occurs, the least squares estimates become inefficient and biased, and it becomes necessary to use alternative methods such as weighted least squares or robust regression. The other options, influential observation and non-independence of errors, are different issues that affect the validity of the regression model, but they do not directly relate to the assumption of constant variance of the error term.

The Least Squares Method Requires That the Variance σz2\sigma _ { z } ^ { 2 }σz2​

The Least Squares Method Requires That the Variance $\sigma _ { z } ^ { 2 }$