Creating Equation Based on Data Set of x,y Values

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Discussion Overview

The discussion revolves around the methods for creating an equation based on a data set of x,y values, specifically focusing on how to project trends beyond the existing data points. Participants explore various modeling approaches suitable for extrapolating data, considering both linear and non-linear trends.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses a desire to derive an equation from a set of x,y values to project future values, acknowledging the need for accuracy beyond simple linear approximations.
  • Another participant suggests that if the trend is not linear, alternative models such as parabolas, exponential functions, or logarithmic functions may be more appropriate for extrapolation.
  • A subsequent reply proposes specific logarithmic models, including variations like y=c*log(x) and y=c*log(x+d), indicating a search for suitable forms of the logarithmic function.
  • Another participant mentions that the choice of model depends on whether the data set consists of measurements or calculated values, recommending regression methods for measurements and polynomial expressions for calculated values, while cautioning about the limitations of polynomial models for predictions outside the original data set.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific modeling approach, as multiple competing views on the appropriate methods for extrapolation remain present throughout the discussion.

Contextual Notes

Participants acknowledge that the effectiveness of different models may depend on the nature of the data set, and there are unresolved considerations regarding the appropriateness of various mathematical approaches for extrapolation.

Zarathuztra
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I'm attempting to reclaim lost knowledge... hopefully this works. I would like to take a data set I have x,y values and project the trend beyond the (10) values I currently have. For example, I have a graph with (10) values for x and y, but would like to graph the trend created by values 1-10 to values 11-15.

I recall learning how to derive an equation to represent the data set but how no idea how I used to to it. Need some help on this one. I'm sure there are other ways to do this that I haven't thought of and wouldn't mind suggestions.

PS, I know I could create a simple linear equation by eyeballing the best fitting slope, but would like to be more accurate as the trend is not always linear.
 
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If the trend is not linear and you want to extrapolate beyond the outermost data points, you'll need some other model ("it is linear" is a model as well). There are many possible models, the best one will depend on your data source. A parabola, an exponential function, a square root, a logarithm, some combination of those, ...
 
In that case I would say the tendency is for logarithmic and exponential. Could you suggest an example model for logarithmic?
 
y=c*log(x)?
y=c*log(x+d)?
y=c*log(x+d)+e?
 
Zarathuztra said:
I'm attempting to reclaim lost knowledge... hopefully this works. I would like to take a data set I have x,y values and project the trend beyond the (10) values I currently have. For example, I have a graph with (10) values for x and y, but would like to graph the trend created by values 1-10 to values 11-15.
As usual, it depends. If the data set is a set of measurements, I would use a form of regression (linear, quadratic, exponential...). If the data is a set of calculated values, you can create a polynomial expression that passes exactly through your data points (but that expression is usually useless in predicting values outside the original data set). I suggest you peruse https://en.wikipedia.org/wiki/Curve_fitting.
 

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