MHB Find Regression Equation for y on x

[Doffy]

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?

 

[Ackbach]

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?

 

[Doffy]

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?

 

[Ackbach]

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.