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# How Do I Find the Uncertainty for Gradient, with Error Bars?

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1. Hey guys,
I have a graph of distance on the x and time on the y axis. I will be finding speed by using 1/gradient. I have custom error bars on excel for the time(obtained by combining random and digital uncertainty). I want to know how to find the uncertainty in the trendline in Excel. I know about the LINEST function, but that doesn't take into account the error bars and only takes into account the x and y values only.

Or should I just use LINEST without the error bars and combine the random and scale/digital reading uncertainties after using LINEST? The thing is, for each value plotted on the graph, the combined uncertainty is not the same so I don't know how I would go about combining these uncertainties with the uncertainty from LINEST. Any help would be appreciated!
2. (Original post by gwagon)
Hey guys,
I have a graph of distance on the x and time on the y axis. I will be finding speed by using 1/gradient. I have custom error bars on excel for the time(obtained by combining random and digital uncertainty). I want to know how to find the uncertainty in the trendline in Excel. I know about the LINEST function, but that doesn't take into account the error bars and only takes into account the x and y values only.

Or should I just use LINEST without the error bars and combine the random and scale/digital reading uncertainties after using LINEST? The thing is, for each value plotted on the graph, the combined uncertainty is not the same so I don't know how I would go about combining these uncertainties with the uncertainty from LINEST. Any help would be appreciated!
You have error bars, which stretch above and below the line of best fit.

Now you need two more gradient lines. One which has the steepest gradient possible to still fit inside the error bars, and one which has the shallowest gradient possible to still fit inside the error bars.

Now you subtract the value of the steepest gradient line from the shallowest gradient line. This is the range. Uncertainty is plus or minus the range.
3. (Original post by Kyx)
You have error bars, which stretch above and below the line of best fit.

Now you need two more gradient lines. One which has the steepest gradient possible to still fit inside the error bars, and one which has the shallowest gradient possible to still fit inside the error bars.

Now you subtract the value of the steepest gradient line from the shallowest gradient line. This is the range. Uncertainty is plus or minus the range.
Thanks for the reply. I checked some of the online notes from Heriott Watt university for Adv Higher Physicsand they are giving me this formula: http://imgur.com/Oenxcic
Which one should I use?
4. (Original post by gwagon)
Thanks for the reply. I checked some of the online notes from Heriott Watt university for Adv Higher Physicsand they are giving me this formula: http://imgur.com/Oenxcic
Which one should I use?
It should be delta m I think. The y intercept should be the same for all three (or two) lines, methinks.
5. (Original post by Kyx)
It should be delta m I think. The y intercept should be the same for all three (or two) lines, methinks.
What relevance does the y intercept uncertainty have? Other than to prove that the best fit line could have passed through the origin?
6. (Original post by gwagon)
What relevance does the y intercept uncertainty have? Other than to prove that the best fit line could have passed through the origin?
Other than that, I don't think it has any.

The question asked for the uncertainty in gradient, and the y-intercept has no effect on the gradient (really), so I would say none. But I am no expert

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