Linearizing a Relation: How to Create a Best Fit Linear Line in Logger Pro

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Discussion Overview

The discussion revolves around the process of linearizing a graph in Logger Pro, specifically how to create a best fit linear line from a dataset. Participants explore various methods for achieving linearization, including transformations and regression techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to linearize their graph and describes their hypothesis regarding the relationship between x and y values.
  • Another suggests taking logarithms of the data and plotting various combinations (log x vs. y, log x vs. log y, x vs. log y) to achieve linearization.
  • A different participant proposes performing a simple linear regression on the (x,y) data, despite acknowledging the underlying nonlinear nature of the relationship. They also mention the possibility of using multiple linear regression to account for the logical relationship.
  • Another participant interprets the request as seeking a function f such that the plot of (y, f(x)) is linearizable, suggesting a form resembling an inverted parabola for the relationship.
  • One participant expresses concern about potentially complicating the discussion and invites clarification if needed.

Areas of Agreement / Disagreement

Participants present multiple competing views on how to approach the linearization of the data, with no consensus reached on a single method or solution.

Contextual Notes

Participants discuss various mathematical transformations and regression techniques without resolving the assumptions or limitations of each approach. The effectiveness of the proposed methods may depend on the specific characteristics of the dataset.

ChanYoung Park
lq5ySf3.png

Hi! Above is a screenshot of logger pro that I'm currently using.
I need to linearise this graph and draw a best fit linear line but I have no clue how to do it. What should I do?
The table on the left shows the raw data. The first column is showing the values for x-axis, and the second is for y-axis. According to my hypothesis, the y-value should initially increase as x-value increases from 0; the y-value is then expected to decrease to zero as x-value increases further.
 

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Try taking the logarithm of the data and plotting them again to see if you can come up with a "linear" line.

So, plot:
  • log x vs. y
  • log x vs. log y
  • x vs. log y
From my experience, that's how you would "linearize" data.
 
If you really want a linear estimator, even though you say that logically it is nonlinear, then you can do a simple linear regression of the (x,y) data. There are many programs to do that.

If you want a linear regression estimator that is not linear, but accounts for the logical relationship, then you can do a multiple linear regression of the data (x, x2, y). I think you will be more satisfied with the result and it will account for the logical relationship that you believe.

The auto-fit line in your graph has done a linear regression on the data (x, x2, x3, x4, x5, y). I think that goes too far and may be unnecessary, but it is more accurate. Here is what I get from y = 40.79166667 +0.67583333*x -0.01772619 *x2.
R_multLinReg.png
 

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Last edited:
Let me see if I understood what you are looking for, please let me know : You want to find f with (y,f(x)) ( where {(y,x)} is your given data ) so that the plot {(y,f(x))} will be linearizable in the sense that it will pass some measure of linear goodness of fit? The plot seemed a bit like an inverted parabola , i.e., ## y-y_0 =c\sqrt x ##, so I considered the linearization ##(x, y_0+c\sqrt x)##. Am I on the right track (finding the right values for ##y_o, c## )?
 
Hey, sorry if I complicated things unnecessarily ; wouldn't be the first time :( . Please
ask a question if so.
 

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