Using the least squares method, determine the correction, in millimeters, to the field difference in elevation along route 1.

• A. +106
• B. +105
• C. +110
• D. +115

Answer: (B)

When you use least squares with a single correction term for all measurements, you’re looking for the constant shift that makes the residuals as small as possible. With one unknown bias added uniformly to every observed field difference, the best estimate is the average (mean) of those observed differences.

So the correction to the field difference along route 1 is simply the average of the measurements. If that average comes out to about +105 millimeters, that is the least-squares correction. It represents the amount you need to add to every measured difference to center the residuals around zero and minimize the sum of squared errors.

The other values would imply a different bias and would not minimize the squared residuals given the data; they would produce a larger overall error than the computed average. A positive correction indicates the measurements were systematically low by that amount, and applying +105 mm brings them in line with the true elevations in the least-squares sense.