MHB Find Regression Equation for y on x

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Determining a regression equation for y on x requires specific data to provide context, as regression analysis is inherently tied to the data being modeled. Without any data, such as a graph or a table, it is impossible to ascertain which of the given equations represents the regression equation. The discussion highlights that regression coefficients and their geometric mean cannot be utilized without context. Both provided linear equations could potentially fit different datasets, but without that information, no conclusion can be drawn. Ultimately, regression analysis necessitates data to be meaningful and applicable.
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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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