Body: <p>Attached image. How would you find the relationship between independent variable (x) and dependent variable (y)? Is it linear or non-linear? What would the function looks like?</p>
  <p>P.S. I believe this is a non-linear regression problem as we are trying to fit a model (function) to this data. I just can't figure out the function. It seems like a mix of positive and negative sigmoid? or quadratic?</p>
  <p><a href="https://i.sstatic.net/sYmVz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sYmVz.png" alt="Updated plot" /></a></p>
  <p>Here is my code I am trying to recreate the plot I saw before:</p>
  <p>import pandas as pd</p>
  <p>#create DataFrame
  df = pd.DataFrame({'x': [0, 1, 2, 3, 11, 12.2, 12.4, 13.9, 14, 15, 4, 10.7, 12.6, 8, 8.5, 9, 13.5, 13.1, 12.8, 5, 15, 14.5, 6, 6.3, 6.6, 7, 7.4, 5.4, 4.4, 3.5, 2.5, 1.5, 0.5],
  'y': [0, 3, 7, 8, 25, 40, 15, 105, -10, -20, 12, 60, 80, 37, 40, 46, 100, 66, 5, 16, 120, 28, 22, 24, 26, 30, 32, 18.5, 14.3, 9.8, 8, 5.2, 1.8]})</p>
  <p>#view DataFrame
  print(df)</p>
  <p>import matplotlib.pyplot as plt</p>
  <p>#create scatterplot
  plt.scatter(df.x, df.y)
  plt.ylabel('Dependent Variable')
  plt.xlabel('Independent Variable')
  plt.title('Function?')
  plt.show()</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-14T10:56:04.330Z
Comments.Text: This does not look like a function. For the same x, it seems the function may produce different $y$s. So, there might be some stochasticity here, or it's just the plot that suggests that it.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-14T13:53:17.983Z
Comments.Text: @nbro Sorry that is my bad. I drew this plot based on what I remember from the similar plot I saw before. There should not be multiple y values per x, so imagine this is a 1 on 1 function. How would you approach this then? what type of activation function does this look like? It must be one from the famous DL activation function family, e.g. logistic, ploynomial, sigmoid, etc. https://en.wikipedia.org/wiki/Activation_function
Comments.UserDisplayName: DLCVIP007
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-14T14:29:59.187Z
Comments.Text: It would be great if you removed the wrong dots then.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-14T14:54:55.983Z
Comments.Text: @nbro I just did. To the best of my knowledge. All I remember is the +120 and -20 on Y axis. and data looked non linear. almost exponential. data was really concentrated up until x=4, then started spreading up and down .
Comments.UserDisplayName: DLCVIP007
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-14T16:07:28.900Z
Comments.Text: Reminds me of this sort of graph: https://graphicmaths.com/img/fractals/fractals/bifurcation/bifurcation-4.png implying you have a system with behaviour phasing between linear and non-linear behaviour, becoming chaotic. If that's the case, accuracy of predictions for x > 4 will necessarily be inaccurate, because precise prediction is impossible
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-15T14:54:55.387Z
Comments.Text: Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
Comments.UserDisplayName: vl_knd
Tags: <machine-learning><regression><sigmoid><non-linear-regression>
Title: Find the relationship between data in this plot
UserDisplayName: DLCVIP007
ThreadText: # Find the relationship between data in this plot
  
  (Asked by: username_0 on 2024-02-14)
  
  Attached image. How would you find the relationship between independent variable (x) and dependent variable (y)? Is it linear or non-linear? What would the function looks like?
  
  P.S. I believe this is a non-linear regression problem as we are trying to fit a model (function) to this data. I just can't figure out the function. It seems like a mix of positive and negative sigmoid? or quadratic?
  
  [![Updated plot](https://i.sstatic.net/sYmVz.png)](https://i.sstatic.net/sYmVz.png)
  
  Here is my code I am trying to recreate the plot I saw before:
  
  import pandas as pd
  
  #create DataFrame
  df = pd.DataFrame({'x': [0, 1, 2, 3, 11, 12.2, 12.4, 13.9, 14, 15, 4, 10.7, 12.6, 8, 8.5, 9, 13.5, 13.1, 12.8, 5, 15, 14.5, 6, 6.3, 6.6, 7, 7.4, 5.4, 4.4, 3.5, 2.5, 1.5, 0.5],
  'y': [0, 3, 7, 8, 25, 40, 15, 105, -10, -20, 12, 60, 80, 37, 40, 46, 100, 66, 5, 16, 120, 28, 22, 24, 26, 30, 32, 18.5, 14.3, 9.8, 8, 5.2, 1.8]})
  
  #view DataFrame
  print(df)
  
  import matplotlib.pyplot as plt
  
  #create scatterplot
  plt.scatter(df.x, df.y)
  plt.ylabel('Dependent Variable')
  plt.xlabel('Independent Variable')
  plt.title('Function?')
  plt.show()
  
  **Tags:** machine-learning, regression, sigmoid, non-linear-regression
  
  > **Comments:**
  > **username_1**: This does not look like a function. For the same x, it seems the function may produce different $y$s. So, there might be some stochasticity here, or it's just the plot that suggests that it.  
  > **username_0**: @username_1 Sorry that is my bad. I drew this plot based on what I remember from the similar plot I saw before. There should not be multiple y values per x, so imagine this is a 1 on 1 function. How would you approach this then? what type of activation function does this look like? It must be one from the famous DL activation function family, e.g. logistic, ploynomial, sigmoid, etc. https://en.wikipedia.org/wiki/Activation_function  
  > **username_1**: It would be great if you removed the wrong dots then.  
  > **username_0**: @username_1 I just did. To the best of my knowledge. All I remember is the +120 and -20 on Y axis. and data looked non linear. almost exponential. data was really concentrated up until x=4, then started spreading up and down .  
  > **username_2**: Reminds me of this sort of graph: https://graphicmaths.com/img/fractals/fractals/bifurcation/bifurcation-4.png implying you have a system with behaviour phasing between linear and non-linear behaviour, becoming chaotic. If that's the case, accuracy of predictions for x > 4 will necessarily be inaccurate, because precise prediction is impossible  
  > **username_3**: Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.  
  
  ---
  
  ## 0 answers
  
  