In least-squares adjustment, the quantity whose squares are minimized is the residuals.

• A. Observations
• B. Residuals
• C. Weights
• D. Measurements

Answer: (B)

In least-squares adjustment, the aim is to achieve the best fit by focusing on the discrepancies between what you observe and what your model predicts. These discrepancies are called residuals—the differences between each observed value and its computed value from the current estimates of the unknowns. The method minimizes the sum of the squares of these residuals, which punishes larger errors more heavily and provides a smooth mathematical objective function.

Weights can come into play in a weighted least-squares formulation, scaling residuals by the confidence you have in each observation. But even then, the quantity being squared remains the residuals; the weights change how much each residual contributes to the total, not what is being squared.

Observations or measurements refer to the data you start with; they are the inputs to the process, not the quantity you minimize.