Question

"In order to estimate the random error in our data, we calculated the average distance between a line of best fit and the collected points. For points R < 4 kpc, we assume a linear curve, and for points R > 4 kpc we assume a flat rotation curve. "

No matter what model of making a best fit curve they use, it doesn’t mean anything physical. The errors bars are just essentially a mathematical quantity. I can slightly tweak the best fit to make error bars smaller or larger as per my wish. So my question is-

1. Is this method of error estimation actually common or the researchers where just lazy here?
2. If this is actually a valid method, what is its physical significance? Like what would these error bars even help me in deciding if I can control them based on my model of fitting.

Answer 1

The method of estimating random error by calculating the average distance between a line of best fit and the collected points is a common technique in data analysis. The physical significance of error bars lies in providing a measure of the uncertainty or variability in the data.

Step-by-step explanation:

The method of estimating random error by calculating the average distance between a line of best fit and the collected points is a common technique in data analysis.

When points with different patterns or behaviors are present in a dataset, it is reasonable to assume different models for different regions of the data. In this case, if data points with R < 4 kpc exhibit a linear behavior and points with R > 4 kpc show a flat rotation curve, it is valid to use these different models for error estimation.

The physical significance of error bars lies in providing a measure of the uncertainty or variability in the data. By considering the range of potential values within the error bars, researchers can assess the reliability of their measurements and determine the level of confidence in their conclusions.