Find Regression Equation for y on x

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Discussion Overview

The discussion revolves around determining a regression equation for y on x based on two linear equations provided, without any accompanying data. The scope includes theoretical considerations of regression analysis and the conditions under which regression equations are meaningful.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant asks how to determine the regression equation from two given linear equations without additional information.
  • Another participant argues that regression equations require context and data to be meaningful, questioning the feasibility of answering the original question without such data.
  • A later reply reiterates the necessity of data for determining a regression equation, stating that both provided equations could represent the best fit for different datasets.
  • One participant suggests that the geometric mean of regression coefficients might be a relevant consideration, despite the lack of context or coefficients.
  • Participants express uncertainty about deriving a regression equation without any data or context.

Areas of Agreement / Disagreement

Participants generally agree that without data, it is impossible to determine which equation serves as the regression equation. Multiple competing views exist regarding the relevance of the geometric mean of regression coefficients.

Contextual Notes

The discussion highlights limitations due to the absence of data and context, which are critical for regression analysis. The implications of the range of the correlation coefficient are mentioned but not resolved.

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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