Finding the error on an intercept, given two points with errors.

In summary, the problem at hand involves finding the error on the y-intercept (a) for two points (x1,y1 and x2,y2) with a one sigma uncertainty of d, assumed to lie on a straight line with a distance L (much greater than d) between them. The equation y = mx + a and the variables \hat{y} = y + \epsilon and \hat{x} = x + \chi may be relevant in solving this problem, but the attempt at a solution has not yet yielded any useful information. Assistance with starting the problem would be greatly appreciated.
  • #1
ghetom
17
0

Homework Statement



(The question is about micro vertex detectors, but I've distilled it into what needs to be done)

You have two points (x1,y1 and x2,y2), assumed to lie on a straight line. The points have a one sigma uncertainty of d. x1 and x2 are separated by a distance L (much greater than d), and x1 is R (plus or minus any error). Find the error on the y-intercept; a.

Homework Equations



[tex]y = mx + a[/tex]
[tex]\hat{y} = y + \epsilon[/tex]
[tex]\hat{x} = x + \chi[/tex]

The Attempt at a Solution



Unfortunantly nothing remotely useful so far...
 
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  • #2
I haven't really started looking into this yet. I'm a bit stuck on where to begin. Any help would be appreciated.
 

Related to Finding the error on an intercept, given two points with errors.

1. How do you find the error on an intercept if only two points with errors are given?

To find the error on an intercept, you can use the formula:
error on intercept = √(error on y-intercept)^2 + (error on slope)^2

2. What are the steps to calculate the error on an intercept using two points with errors?

The steps to calculate the error on an intercept using two points with errors are:
1. Determine the error on the y-intercept and slope for each point
2. Square each error value
3. Add the squared error values together
4. Take the square root of the sum to find the error on the intercept

3. Can the error on an intercept be negative?

No, the error on an intercept cannot be negative. It represents the uncertainty or range of possible values for the y-intercept and must be a positive value.

4. What is the relationship between the error on an intercept and the error on the slope?

The error on an intercept and the error on the slope are two independent values that are combined to determine the overall uncertainty in a linear regression model. They are used to calculate the overall error on the predicted values.

5. How does the size of the error on the points affect the error on the intercept?

The size of the error on the points has an impact on the error on the intercept. Generally, the larger the errors on the points, the larger the error on the intercept will be. This is because larger errors on the points indicate a greater uncertainty in the data, which can lead to a wider range of possible values for the y-intercept.

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