uncertainty on best fit gradient
I have a plot of some data points that have error bars on the y axis.
A bit of software I am using gives me the gradient and a "Standard Error", but it doesn't take the size of error bars into consideration. I'm assuming that it just looks at how well the gradient fits the data points to give the standard error on the gradient.
But doesn't one need to take into consideration the size of the error bars on the data points??
Re: uncertainty on best fit gradient
Typically we have a few different kinds of standard errors.
For a regression we have a standard error for the actual estimated parameter, but we can also have conditional standard errors for some particular set of values and this is a bit different. These are calculated in different ways.
You can also have standard errors that are from the sample data.
Together, all of these different standard errors can refer to different things and the one you look at is the one that is most suited for the problem you are working on.