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

[ChanYoung Park]

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.

 

[CivilSigma]

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.

 

[FactChecker]

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.

 

[WWGD]

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 $y_o, c$ )?

 

[WWGD]

Hey, sorry if I complicated things unnecessarily ; wouldn't be the first time :( . Please
ask a question if so.