Math CentralQuandaries & Queries


Question from catherine, a student:

Given a set of data values ,we can get two regression lines .Explain.

Hi Catherine,

Suppose that you have data on two variables $x$ and $y.$ I think that what is expected is that you can ask for a regression line with $x$ as the independent variable, $ y = a + b x$ or a regression line with $y$ as the independent variable $x = c + d y.$

The power of regression is that you can use the equation obtained to make statistically predictions about the dependent variable for various values of the independent variable. For these predictions to be valid there are certain assumptions that the independent and dependent must satisfy. You can use the data to obtain two regression lines as I claim above but at most one of the choices of independent and dependent variables would allow for the necessary assumptions to be satisfied.



Indeed, we can get many regression lines - least squares, neutral regression, resistant fit, weighted regression, and more. But I assume you mean regressing X as a function of Y and Y as a function of X, both of which can be done with a pocket calculator.

As they make different assumptions about where any errors lie, these models give different lines unless the data are perfectly correlated.

Good Hunting!

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