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Do you regress Y on X or X on Y?
If y represents the dependent variable and x the independent variable, this relationship is described as the regression of y on x. The relationship can be represented by a simple equation called the regression equation.
What does it mean to regress X against Y?
to determine the extent to which a given dependent variable (y) can be explained or predicted by a number of independent variables (xs). That is, the researcher may regress y on x. …
How to regress y on X and vice versa?
And in general: How do I choose to regress which one on which: Just simple when I’m interested in y then I regress y on x and vice versa? Find a surface parametrized by X such that when values of Y are projected on the surface, the sum of squared distances of Y from the surface X measured along the projections get minimized.
Is the relationship between linear regression on Y and X the same?
This suggests that doing a linear regression of y given x or x given y should be the same, but I don’t think that’s the case. Can someone shed light on when the relationship is not symmetric, and how that relates to the Pearson correlation coefficient (which I always think of as summarizing the best fit line)?
What do you need to know about regression?
What you are trying to do in regression is find what might be called the ‘line of best fit’. However, while this seems straightforward, we need to figure out what we mean by ‘best’, and that means we must define what it would be for a line to be good, or for one line to be better than another, etc. Specifically, we must stipulate a loss function.
Which is the slope of the regression line?
The correlation coefficient, r, is the slope of the regression line when both variables have been standardized first. That is, you first subtracted off the mean from each observation, and then divided the differences by the standard deviation.