<p>I think you are mixing up a few things.</p>
<ul>
<li>Correlation is not a prerequisite for regression; in fact, regression can be used to investigate whether there is a correlation between parameters, and by how much, and whether it is significant or not.</li>
<li>Sufficient power is also not an assumption for regression. Although it's of course good to have a sufficiently powered study, you can do regression on any data set regardless of the variance and <em>n</em>.</li>
<li>The issue of linearity is indeed an assumption for linear regression. If linearity is not met you can try <a href="https://sciences.usca.edu/biology/zelmer/305/trans/" rel="nofollow noreferrer"><strong>transforming the independent variable</strong></a> to linearize the relation. Transformation of the dependent is not recommended, because the variance will change along the way. Alternatively, you can use nonlinear regression to fit a curve through the data and obtain the regression parameters you are after from that.</li>
</ul>
<p><a href="https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/statistics/regression-and-correlation/assumptions-of-regression-analysis.html" rel="nofollow noreferrer">Here is link</a> summing up the assumptions of regression analysis.</p>

CC BY-SA 4.0
2024-09-12T13:08:32.280Z
2024-09-13T14:47:43.590Z
2024-09-13T14:47:43.590Z
AliceD
<p>In our master's thesis, our goal was to model several (partially multiple) linear regressions. However, some of the assumptions were not met, such as the linearity of the variables. Additionally, some of the variables do not correlate significantly with each other. A possible reason for the violation of the assumptions could be the insufficient sample size (power analysis suggested N = 124, actual N = 74). Are there alternatives for how we can still establish a regression model?</p>
<p>We are conducting all analyses in SPSS.</p>
<p>Thank you very much for your help!</p>

CC BY-SA 4.0
2024-09-12T21:20:53.307Z
Statistics is not magic, it's a set of tools to work with data. If you're using the tools of power analysis properly, and those tools tell you that you don't have enough data for your research question, then that's your problem. It's not worth testing other assumptions, if you do not have the data, you cannot conjure more data out of thin air with statistics. Or, rather, it's less about what you "can" and can't do, and whether your interpretations of what you've done will have any meaning. You can certainly "establish a regression model" with whatever you have, it just might not be useful.
Bryan Krause
CC BY-SA 4.0
2024-09-12T21:27:08.787Z
Most often in psychology, people use statistics to test inferential research questions like "are these groups different?" or "is there a non-zero relationship between these two variables?" using null-hypothesis testing. In that sense it is wrong to think "variables do not correlate significantly" is a *problem*. The point of doing a statistical test would be to be able to make a conclusion about whether a correlation is significant or not. If you only plan to bother with things that *are* significant, you're not using data to learn, you're just reinforcing what you already believe.
Bryan Krause
CC BY-SA 4.0
2024-09-12T21:29:18.767Z
You are absolutely not alone in these misunderstandings of statistics, you'll find them in many many published papers. But it sounds like where you are at in your understanding right now is not at a place where you're really ready to assess regression assumptions, you need to take a few steps back and understand what it is you're doing with regression at all in the first place. That might include revisiting a course on statistics or it might involve consulting with a statistician. As a student, it should also involve consulting with your mentor.
Bryan Krause
<methodology><statistics><psychology><analysis><regression>
Dealing with regression assumption Issues
Svenja Bornand
# Dealing with regression assumption Issues

(Asked by: username_0 on 2024-09-12)

In our master's thesis, our goal was to model several (partially multiple) linear regressions. However, some of the assumptions were not met, such as the linearity of the variables. Additionally, some of the variables do not correlate significantly with each other. A possible reason for the violation of the assumptions could be the insufficient sample size (power analysis suggested N = 124, actual N = 74). Are there alternatives for how we can still establish a regression model?

We are conducting all analyses in SPSS.

Thank you very much for your help!

**Tags:** methodology, statistics, psychology, analysis, regression

> **Comments:**
> **username_1**: Statistics is not magic, it's a set of tools to work with data. If you're using the tools of power analysis properly, and those tools tell you that you don't have enough data for your research question, then that's your problem. It's not worth testing other assumptions, if you do not have the data, you cannot conjure more data out of thin air with statistics. Or, rather, it's less about what you "can" and can't do, and whether your interpretations of what you've done will have any meaning. You can certainly "establish a regression model" with whatever you have, it just might not be useful.  
> **username_1**: Most often in psychology, people use statistics to test inferential research questions like "are these groups different?" or "is there a non-zero relationship between these two variables?" using null-hypothesis testing. In that sense it is wrong to think "variables do not correlate significantly" is a *problem*. The point of doing a statistical test would be to be able to make a conclusion about whether a correlation is significant or not. If you only plan to bother with things that *are* significant, you're not using data to learn, you're just reinforcing what you already believe.  
> **username_1**: You are absolutely not alone in these misunderstandings of statistics, you'll find them in many many published papers. But it sounds like where you are at in your understanding right now is not at a place where you're really ready to assess regression assumptions, you need to take a few steps back and understand what it is you're doing with regression at all in the first place. That might include revisiting a course on statistics or it might involve consulting with a statistician. As a student, it should also involve consulting with your mentor.  

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## 1 answers

### Answer by username_2 on 2024-09-12. Score: 1

I think you are mixing up a few things.

* Correlation is not a prerequisite for regression; in fact, regression can be used to investigate whether there is a correlation between parameters, and by how much, and whether it is significant or not.
* Sufficient power is also not an assumption for regression. Although it's of course good to have a sufficiently powered study, you can do regression on any data set regardless of the variance and *n*.
* The issue of linearity is indeed an assumption for linear regression. If linearity is not met you can try [**transforming the independent variable**](https://sciences.usca.edu/biology/zelmer/305/trans/) to linearize the relation. Transformation of the dependent is not recommended, because the variance will change along the way. Alternatively, you can use nonlinear regression to fit a curve through the data and obtain the regression parameters you are after from that.

[Here is link](https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/statistics/regression-and-correlation/assumptions-of-regression-analysis.html) summing up the assumptions of regression analysis.


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