# Graph uncertainty

Identity
If you have several data points, each with a small uncertainty in the y-direction, and you want to find the uncertainty in the gradient and the uncertainty in the intercepts of the line of best fit, how would you go about doing that?

*I know with many points you would have to do something with regression, but could the simple, 2-data point case also be explained?

Here's what I'm thinking so far for the 2-data point case, can someone please tell me if i'm right:

Equation of the line, including uncertainties:

$$y -(y_0 \pm U(y_0)) = \frac{y_1 \pm U(y_1) - (y_0 \pm U(y_0))}{x_1 - x_0}(x - x_0)$$

So you would eventually get two separate "uncertainty" bits, one in the gradient and the other in the constant term.

$$y = (m \pm U(m))x + C \pm U(C)$$

Now do you just let 'y' or 'x' equal 0 and solve?

Thanks so much

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## Answers and Replies

jackiefrost
Wouldn't the best fit line for just two data points points, regardless of the uncertainties in the two points' y values, be a line through the two points themselves since their y values would necessarily be centered in the y error range? Therefore, wouldn't the gradient just be the slope of the line through the two points?