Data Transformation for Non-linear Feature in Linear Regression I am new to various types of non-linear data transformations. I am sorry if this question is too basic for experts. I read (https://stattrek.com/regression/linear-transformation.aspx) that there are various types of transformations available:

*

*Exponential

*Logarithmic

*Polynomial (Quadratic, cubic etc.)

*Inverse

*Sine/cosine

I want to intuitively understand which transformation should I use. I know that if the data has zeros in the dependent variable, then we cannot really use the exponential transformation. Similarly, the logarithmic transformation won't work if there are zeros in the independent variable. Moreover, I read somewhere that the log transformation is used to reduce the effect of outliers. That's all I know.
I want to be able to intuitively understand which transformation I should use given the distribution.
For instance, here's the sample transformation from the original data. I cannot share original data because of confidentiality, so I created a representative dataset below in Python.
import numpy as np

ylist = [1]*6+[2]*12+[3]*18+[4]*15+[5]*11+[6]*6+[7]*3+[8]*2+[9]+[10]+[11]*2+[12]*3
tlist = np.arange(80)

import matplotlib.pyplot as plt

plt.title('Distribution')
plt.hist(ylist, bins=100)
plt.show()

Can someone please guide me on whether I should use the exponential, logarithmic, polynomial, or inverse transformation? I know that one can experiment with these transformations to see which one fits well. However, this method isn't scalable if we have a few features. Often times, I end up hitting a wall and feel that I lack intuitive understanding of which transformation should be used in what situation.
Hence, my goal is to understand the reason and general guidelines for picking one transformation over the other. I'd appreciate your thoughts. Can someone please help me?
Here's the distribution/output of Python code:

 A: If I understand well you're trying to intuitively know what would be the best fit to these data ? In this case you have to find the global dynamic of the possible function : are the values reaching a constant value ? Are they increasing at a constant/varying rate ? Is the rate changing sign ?
Here for example, the increase rate is changing sign (it's increasing then decreasing and then increasing again). So neither exp or log or inverse functions are good to make a fit, because the increasing rate (which is basically the derivative of the function) has a constant sign. Here you have to fit either a trigonometric function of a polynomial function.
The sin and cos are basically for periodic (or pseudo-periodic) sets, and here it's not obvious that we have periodic oscillations. Since we have 2 extrema here, I would go with a third-degree polynomial function, (number of extrema +1 = minimal degree to fit). Also, it's important to note that fitting with a high degree polynomial function is not interesting since it won't enlighten you on the general behavior of the set.
