Hi, I hope I'm asking this in the right place. I need to understand this in order to complete a project, but it's not exactly a 'homework question'.(adsbygoogle = window.adsbygoogle || []).push({});

I have some data which has a linear trend. The x values all have the same (random) uncertainty of ≈5cm and the y values all have the same random uncertainty of ≈0.5ms

I've got all my data plotted on graphs using a spreadsheet, which can put a best-fit line (of the form y=mx+c) through the points and tell me the equation of the line. I need to be able to propagate my errors through though, as I need to find the inverse of the gradient and the error associated with that in order to get the result I'm interested in. I also want to find the y value at which the best fit line crosses a certain x value (ie. the y-intercept) and its error.

I have a very basic understanding of statistics - standard deviation, averages, simple error propagation, and I understand that the best-fit lines are found using linear regression.

I've attached one of my graphs.

Background:

I'm in my second year of university, studying geophysics. This is my first fieldwork project which is a refraction seismology survey, and I'm interested in finding out the velocity at which the wave travels through the ground (velocity = 1000/gradient, in these graphs). In the graph I've posted, the source of the waves is at 48 m and the graph shows the wave travelling in forward and backward directions and refracting in response to subsurface changes.

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# Uncertainties in gradients and best-fit lines

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