Determining Min & Max Slopes w/Varying STDEV

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In summary, the conversation discusses using simple linear regression analysis with individual standard deviations for each data point to calculate the maximum and minimum slope of a graph. One suggestion is to modify the data points by increasing and decreasing them based on their standard deviations in order to determine the maximum and minimum slopes. The validity of this method is questioned, and the possibility of using Weighted Least Squares is mentioned.
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Salish99
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If I have a slope for which I do simple linear regression analysis, but each of the 6 datapoints of the slope have their individual (non-equal) standard deviations, how can I calculate the maximum and minimum slope of the graph?
One idea we too up was to increase the first half of the data points by the standard deviation, and decrease the other have by their standard deviations (and vice versa) in order to determine the maximum and minimum slopes from the resulting data points.
Is such an analysis valid? What else could I do to determine the maximum and minimum slopes based on the individual standard deviations?
If my explanation was unclear I have attached a document with simple made-up values for representation of the issue:
http://drop.io/stats20100/asset/minmax-gif"
This example data was created for simple commenting, the actual data is more complex.
Below the values used for this example:

x y σ, % σ y-σ y+σ MINsl MAXslope
1 1 10 0.1 0.9 1.1 1.1 0.9
2 2 20 0.4 1.6 2.4 2.4 1.6
3 3 10 0.3 2.7 3.3 3.3 2.7
4 4 10 0.4 3.6 4.4 3.6 4.4
5 5 20 1.0 4.0 6.0 4.0 6.0
6 6 10 0.6 5.4 6.6 5.4 6.6

LINEST
1 0 AVG
0.76 0.64 MIN
1.24 -0.64 MAX
 
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Salish99 said:
each of the 6 datapoints of the slope have their individual (non-equal) standard deviations

Is "Weighted Least Squares" what you were looking for?
 

1. What is the purpose of determining the minimum and maximum slopes with varying standard deviation?

The purpose of determining the minimum and maximum slopes with varying standard deviation is to identify the range of possible slopes for a given dataset. This information can be used to understand the variability of the data and make informed decisions about the relationship between variables.

2. How is the standard deviation used in determining the minimum and maximum slopes?

The standard deviation is used to calculate the confidence interval for the slopes. This interval represents the range in which the true slope is likely to fall with a certain level of certainty. By varying the standard deviation, we can see how the confidence interval and therefore, the minimum and maximum slopes, change.

3. What factors can affect the minimum and maximum slopes with varying standard deviation?

The main factor that can affect the minimum and maximum slopes with varying standard deviation is the amount of variability in the data. The more spread out the data points are, the wider the confidence interval and the larger the range of possible slopes. Other factors may include the sample size and the distribution of the data.

4. How can determining the minimum and maximum slopes with varying standard deviation be useful in a scientific study?

Determining the minimum and maximum slopes with varying standard deviation can be useful in a scientific study by providing insight into the strength and direction of the relationship between variables. It can also help identify potential outliers or influential data points that may be affecting the slope. This information can be used to draw more accurate conclusions and make more informed decisions.

5. Are there any limitations to using standard deviation to determine the minimum and maximum slopes?

Yes, there are limitations to using standard deviation to determine the minimum and maximum slopes. Standard deviation is based on assumptions about the distribution of the data and may not be appropriate for all types of data. Additionally, it only takes into account the variability in the y variable and not the x variable. Other methods, such as regression analysis, may be more appropriate for certain types of data and provide a more comprehensive understanding of the relationship between variables.

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