MHB Find Regression Equation for y on x

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SUMMARY

The discussion centers on determining the regression equation of y on x using two linear equations: 2x + y = 13 and 2x + 5y = 20. Participants emphasize that regression equations require contextual data, such as a dataset or graph, to be meaningful. Without this data, it is impossible to ascertain which equation serves as the best fit. The conversation highlights the importance of having regression coefficients and context for accurate analysis.

PREREQUISITES
  • Understanding of linear equations and their graphical representations.
  • Familiarity with regression analysis concepts.
  • Knowledge of regression coefficients and their significance.
  • Basic statistical principles, including correlation coefficients.
NEXT STEPS
  • Study the principles of linear regression analysis using tools like R or Python's scikit-learn.
  • Learn how to interpret regression coefficients in the context of data analysis.
  • Explore methods for visualizing data to identify potential regression models.
  • Research the geometric mean of regression coefficients and its applications in statistics.
USEFUL FOR

Statisticians, data analysts, and students studying regression analysis who seek to understand the importance of context and data in determining regression equations.

Doffy
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How do I determine the regression equation when not much information is given? For example:
Given the following equations:
2x + y = 13
2x + 5y = 20,

which one is the regression equation of y on x?
 
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Regression equations only make sense in the context of data that you're trying to explain using some model. Your question is quite impossible to answer unless there is some data present. Were you given, say, a graph of some data? Or a table of data?
 
Ackbach said:
Regression equations only make sense in the context of data that you're trying to explain using some model. Your question is quite impossible to answer unless there is some data present. Were you given, say, a graph of some data? Or a table of data?

Well, I am afraid that no further information of any kind is available.
However, I was wondering that since regression coefficient is the geometric mean of the regression coefficients, can we use this fact to determine our equation?
Also that, the range of r is -1$$\le$$ r $$\le$$ +1. Is it possible?
 
We have no regression coefficients, we have no context. Your question is completely impossible to answer as is, I'm afraid. Both linear equations you've given could easily be the best fit line for a particular data set; but without that data set, there's no way to tell which line would fit the data better.
 

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