What characterizes weighted least squares?

• A. It minimizes the sum of squared residuals without weights.
• B. It assumes equal variance across observations.
• C. It estimates parameters using weighted least squares, often weighting by the inverse of the variance.
• D. It is identical to ordinary least squares.

Answer: (C)

Weighted least squares is a method for estimating regression coefficients when the variability of observations differs across cases (heteroscedasticity). Instead of minimizing the plain sum of squared residuals, you minimize the sum of squared residuals weighted by how precise each observation is. In practice, those weights are usually the inverse of the observations’ variances, so data points with higher uncertainty contribute less to the estimate and those with lower uncertainty contribute more. This approach yields more efficient, reliable estimates when variances differ. If every observation had the same variance, the weights become the same for everyone and weighted least squares behaves like ordinary least squares. So the statement that parameter estimates come from weighted least squares, typically weighting by the inverse of the variance, accurately describes the method.