Jordan's Question from Facebook (About Regression)

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SUMMARY

Jordan from Facebook discusses the application of a specific regression model defined as y = A + B·e^x. He emphasizes the transformation of the variable by setting X = e^x, which simplifies the equation to a linear form y = A + B·X. The key conclusion is that by evaluating e^x at each point x, one can create a new dataset X, enabling the use of linear least squares regression to analyze the relationship between y and X effectively.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with linear regression techniques
  • Knowledge of least squares regression methodology
  • Proficiency in data transformation and manipulation
NEXT STEPS
  • Study the principles of linear least squares regression in depth
  • Learn about data transformation techniques, specifically exponential transformations
  • Explore statistical software tools for performing regression analysis, such as R or Python's SciPy library
  • Investigate the implications of model assumptions in regression analysis
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Data scientists, statisticians, and analysts interested in regression modeling and data transformation techniques will benefit from this discussion.

Sudharaka
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Jordan from Facebook writes:

Help please,

2yod9uh.jpg
 
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Sudharaka said:
Jordan from Facebook writes:

Help please,

2yod9uh.jpg

If we assume that a model of the form [math]\displaystyle \begin{align*} y = A + B\,e^{x} \end{align*}[/math] is appropriate, then we note that if we have [math]\displaystyle \begin{align*} X = e^{x} \end{align*}[/math], then we have a nice linear equation [math]\displaystyle \begin{align*} y = A + B\,X \end{align*}[/math].

So it would help to start by evaluating [math]\displaystyle e^x [/math] at each point x, giving a new set of data which we can call X. Then perform a linear least squares regression for data set y against data set X.
 

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