In Weighted Least Squares, what is the purpose of the weights?

• A. To give more weight to observations with higher variance
• B. To give equal weight to all observations
• C. To reflect the inverse of the variance of observations
• D. To minimize the number of observations

Answer: (C)

In Weighted Least Squares, the weights adjust for differences in precision across observations. Each observation gets a weight proportional to the inverse of its error variance, so observations with smaller variance (more reliable data) have more influence, and those with larger variance have less. This makes the estimates more efficient when variances differ, since the model pays more attention to the more precise data. If you were to weight higher-variance observations more, you’d be allowing noisier data to drive the estimates; giving equal weight ignores precision differences; and reducing the number of observations isn’t achieved through weighting.