<p>My partner and I did some computation on the Tully Fisher relation at uni.</p>

<p>In that, the slope of the logarithm plot between the luminosity and rotational velocity, was 2.6.</p>

<p>Now, that slope corresponds to the exponent to which <span class="math-container">$v_{rotation}$</span> is raised to. i.e.</p>

<p><span class="math-container">$$L=Av_{rotation}^b$$</span></p>

<p>where <span class="math-container">$b$</span> is the exponent.</p>

<p>So, <span class="math-container">$b$</span> officially is close to 4. And I have used up a sample size of over 10 galaxies. And the plot looked pretty shabby honestly. Is our result poor?</p>

<p><a href="https://i.sstatic.net/cJPOT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cJPOT.png" alt="enter image description here"></a> </p>

CC BY-SA 4.0
2020-03-05T22:08:57.670Z
What exactly would be the question to which you would like an answer? Help with estimating the uncertainty in the slope?
uhoh
CC BY-SA 4.0
2020-03-05T22:10:56.103Z
No. Is the data authentic enough to actually be legitimiate? Because only four out of those points actually meet the red line. And so, I was wondering if this was in fact a bad fit, then the uncertainties of the data points have to be re done.
Karthik
CC BY-SA 4.0
2020-03-05T22:24:16.743Z
Okay thanks! I think that an answer will end up explaining how to calculate the uncertainty in the slope and/or a "goodness of fit" metric and recommend how you can decide for yourself if those indicate a result that is good or poor. Science is science, if this is the data, then this is the data. If it fits a line, it fits, if it doesn't it doesn't. We don't "re do" data points to make the fit better, that's a *science no-no!* :-)
uhoh
CC BY-SA 4.0
2020-03-05T22:27:26.600Z
If those are +/- 1 sigma (one standard deviation) error bars, then as a rule of thumb the fitting function should pass through roughly 2/3 of them on average, which would be about 6 out of 9 here. But that's just an average, if you did ten different data sets,  sometimes you'll see only 3 out of 9 like you have here.
uhoh
CC BY-SA 4.0
2020-03-06T03:39:26.847Z
@uhoh thanks so much mate. I needed a bit of a breather. Is it normal to produce "not-so-correct" results the first time in astronomy?
Karthik
CC BY-SA 4.0
2020-03-06T03:46:54.240Z
All I can say is that [these are the wrong questions](https://youtu.be/CQ-I2qa0ZQY?t=10)
uhoh
CC BY-SA 4.0
2020-03-06T10:07:05.623Z
Data are data. All you need to do is discuss the errors, the goodness of fit and possibly what you can do during further measurements to get data and fit /theory match better. Look what contributed to the errors of the individual data points. Look at the error of the slow of your fit
planetmaker
CC BY-SA 4.0
2020-03-06T15:59:07.310Z
You don't say what bandpass the luminosity was measured in. Slopes of closer to 3 are seen when using optical (especially blue) luminosities. And given that you have only nine data points, you shouldn't expect a very accurate result anyway.
Peter Erwin
CC BY-SA 4.0
2020-03-10T03:25:30.960Z
@planetmaker and Peter Erwin ya I do realise that now. thanks.
Karthik
<radio-astronomy>
Slope of log plot of luminosity-velocity in Tulley Fisher relation
Karthik
# Slope of log plot of luminosity-velocity in Tulley Fisher relation

(Asked by: username_0 on 2020-03-05)

My partner and I did some computation on the Tully Fisher relation at uni.

In that, the slope of the logarithm plot between the luminosity and rotational velocity, was 2.6.

Now, that slope corresponds to the exponent to which $v\_{rotation}$ is raised to. i.e.

$$L=Av\_{rotation}^b$$

where $b$ is the exponent.

So, $b$ officially is close to 4. And I have used up a sample size of over 10 galaxies. And the plot looked pretty shabby honestly. Is our result poor?

[![enter image description here](https://i.sstatic.net/cJPOT.png)](https://i.sstatic.net/cJPOT.png)

**Tags:** radio-astronomy
> **Comments:**
> **username_1**: What exactly would be the question to which you would like an answer? Help with estimating the uncertainty in the slope?  
> **username_0**: No. Is the data authentic enough to actually be legitimiate? Because only four out of those points actually meet the red line. And so, I was wondering if this was in fact a bad fit, then the uncertainties of the data points have to be re done.  
> **username_1**: Okay thanks! I think that an answer will end up explaining how to calculate the uncertainty in the slope and/or a "goodness of fit" metric and recommend how you can decide for yourself if those indicate a result that is good or poor. Science is science, if this is the data, then this is the data. If it fits a line, it fits, if it doesn't it doesn't. We don't "re do" data points to make the fit better, that's a *science no-no!* :-)  
> **username_1**: If those are +/- 1 sigma (one standard deviation) error bars, then as a rule of thumb the fitting function should pass through roughly 2/3 of them on average, which would be about 6 out of 9 here. But that's just an average, if you did ten different data sets,  sometimes you'll see only 3 out of 9 like you have here.  
> **username_0**: @uhoh thanks so much mate. I needed a bit of a breather. Is it normal to produce "not-so-correct" results the first time in astronomy?  
> **username_1**: All I can say is that [these are the wrong questions](https://youtu.be/CQ-I2qa0ZQY?t=10)  
> **username_2**: Data are data. All you need to do is discuss the errors, the goodness of fit and possibly what you can do during further measurements to get data and fit /theory match better. Look what contributed to the errors of the individual data points. Look at the error of the slow of your fit  
> **username_3**: You don't say what bandpass the luminosity was measured in. Slopes of closer to 3 are seen when using optical (especially blue) luminosities. And given that you have only nine data points, you shouldn't expect a very accurate result anyway.  
> **username_0**: @planetmaker and Peter Erwin ya I do realise that now. thanks.  

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## 0 answers

