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What is a line of best fit and what does it mean?
Any reported data should have an uncertainty with it so the reader has some idea of the validity of the information. When writing a conclusion you would usually refer to the intercept and the gradient, both of these have associated uncertainties, and these are important.
Why is this important?
Here is an example of a graph which was used as the basis for a conclusion stating a proportional relationship. Do you agree?
You could produce a positive, zero, or negative gradient whilst staying within the error bars given.
Without the uncertainties this could be reported as a positive trend.
So how do we use uncertainties to explain to the reader how valid our data is?
Once we have error bars plotted we can draw as many gradients as we wish that pass through most of the points or their error bars. Here I have stopped at an exra 4 but I could draw many more.
However, for the uncertainties we just need the range (the maximum and minimum) so we would just plot these two extra gradients.
Then we use the same method as before to work out the experimental uncertainty for the gradient and intercept, giving:
m = 6 ± 6 s/mL
c = 25 ± 9 s
The percentage uncertainty of the gradient is a useful indicator of the validity of the method - 100% uncertainty suggests the method could be improved.
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