If you have any further questions, feel free to ask.

In summary, the conversation discusses different methods for calculating the error uncertainty of a slope when given a set of data points with associated uncertainties. The person mentions their previous method of finding the uncertainty by subtracting the maximum and minimum possible slopes, but notes that it may not be accurate. They then ask if anyone knows of a better method and provide a resource for weighted least squares straight line fitting as a potential solution.
  • #1
johnnnnyyy
16
0
So I am a little confused about how to calculate the error uncertainty of a slope. Let's say I have data points (1,2), (2,2.75), (3,3.75), (4,4.7), (5,5.5) which when put in excel gives me a slope of .895. Let's say the error uncertainty for every point is +/-0.1. What I used to do is subtract the maximum possible slope of the first and last points and the minimum possible slope and divide it by 2 to find the error uncertainty. So the max slope would be ((5.5+.1)-(2-.1))/((5-.1)-(1+.1)) and then I would basically do the opposite to find the min slope. But recently I discovered that it is not an accurate way to find the uncertainty of the slope.

Does anybody else no how to find the error uncertainty of a slope?
 
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  • #2
This appears to be what you're looking for:

https://www.che.udel.edu/pdf/FittingData.pdf‎

Since your data points have uncertainties associated with them (more precisely, with their "y-values"), scroll down to the section Weighted Least Squares Straight Line Fitting which begins on page 8. It might help to skim through the preceding pages first.
 
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Related to If you have any further questions, feel free to ask.

## 1. What is "error uncertainty of slope"?

The error uncertainty of slope, also known as the standard error of the slope, is a measure of the variability or uncertainty in the slope of a regression line. It represents the amount of error that may be present in the estimated slope of a data set, and is typically expressed as a percentage or in the same units as the data.

## 2. How is the error uncertainty of slope calculated?

The error uncertainty of slope is calculated using a formula that takes into account the standard deviation of the y-values, the standard deviation of the x-values, and the correlation coefficient of the data. This formula is typically provided by statistical software programs, but can also be calculated manually using mathematical equations.

## 3. Why is the error uncertainty of slope important?

The error uncertainty of slope is important because it provides information about the accuracy and reliability of the slope estimate in a regression analysis. It allows researchers to determine the range of values in which the true slope is likely to fall, and to make appropriate interpretations and conclusions based on the data.

## 4. How does sample size affect the error uncertainty of slope?

The error uncertainty of slope is inversely proportional to the sample size. This means that as the sample size increases, the error uncertainty of slope decreases, and vice versa. This is because larger sample sizes provide more data points, resulting in a more precise estimate of the slope.

## 5. Can the error uncertainty of slope be reduced?

Yes, the error uncertainty of slope can be reduced by increasing the sample size, improving the quality of the data, and reducing the variability of the data. Additionally, checking for outliers and influential data points and using appropriate statistical methods can also help to reduce the error uncertainty of slope.

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