Percent deviation for linear regression

Question

I have 2 sets of experimental data to which I applied a linear fit using Matlab. I can use the slope value to compare between both of them.

My question is: can I use the following percent deviation equation for the linear fit to compare between these 2 sets?

$$ \%\text{ deviation} = \frac{\text{last point - first point}}{\text{last point}}\times 100$$

The first point of the linear fitting when (x=0), the last point where my data end (x=311 in this example)

In this example the slope is -0.01569 and the %deviation is -4.063%.

You can do whatever you want, but maybe better tell us what are you trying to achieve with this..? If you want to compare the slopes, why not just do this? — Tim, Commented Mar 9, 2023 at 14:34

Mr Pi · Accepted Answer · 2016-12-20 21:38:01Z

0

The results are different from the slope results. Example:

Let's say your sets both consist of 2 points.

Set a: y1=0 y2=1 Set b:y1=4 y2=5

Slopes are both equal to 1. But a%=100% b%=20%

Edit: Another problem arises if the two sets are not of equal length.

answered Dec 20, 2016 at 21:28

Mr Pi

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$\begingroup$ Thanks for your answer, The linear regression slope also have the same problem if the lengths are not equal. in my opinion (I don't know if it's correct or not) the %deviation shows how much the %change between the start condition and the last condition. if your presented data are representing 2 cars speed then the first one has changed 100% from 0 speed to 1, while the second car changed speed by only 20% from 4 to 5, the slope shows the increasing or decreasing while the %change shows the change from the start condition. (forgive my bad English). $\endgroup$
– Mustafa Mahmood
Commented Dec 21, 2016 at 13:54
$\begingroup$ @MustafaMahmood The slope shows the absolute increase per unit of the x-axis. The %deviation shows the percentual increase per unit of the x-axis. $\endgroup$
– Mr Pi
Commented Jan 3, 2017 at 14:15

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