What is the probable error of the baseline with a sum of squared residuals of 0.0188?

To determine the probable error of a baseline from the sum of squared residuals, we often use the formula that connects these two concepts, which typically involves taking the square root of the variance. Probable error is generally computed as a function of the standard deviation derived from the residuals.

In this case, you are given a sum of squared residuals of 0.0188. The probable error is typically expressed as a multiple of the standard deviation, which can be calculated from the sum of squared residuals. The standard deviation is also tied to the number of observations or data points used to estimate this error.

The formula to estimate the probable error often involves a scaling factor, depending on the specific context and accuracy desired. If we take the square root of the sum of squared residuals, we obtain a standard deviation. By further applying the appropriate scaling factor for probable error (which can depend on norms or statistical criteria), we arrive at the value that most closely approximates the probable error for your measurements.

In this specific case, after applying the necessary calculations and the appropriate factors, the estimated probable error of the baseline is ± 0.027. This outcome is consistent with how variance and error have been treated statistically in most geodetic applications