What does it mean for regression to only be normally distributed in the vertical direction and correlation to be normally distributed in horizontal and vertical directions?

Mathe

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It would be a lot easier if you told us where did you find these statements. As it is, 'correlation being normally distributed' does not make sense. A correlation is a statistical measure (of theoretical quantity) that measures the degree of dependence between two sets of paired observations (or random variables). Typically, this measure is bounded between 1 and -1, so not even the sampling version of correlation could ever be normally distributed. I fear this statement is missing context.

Faithalone

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My bad. I read this from my class noted and I rewrote it from memory incorrectly. What I meant to say was that correlation assumes data is normally distributed in the vertical direction and regression assumes data is normally distributed in the horizontal and vertical directions.

Mathe

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I think you have it backwards. Regression only assumes the y or vertical axis is normally distributed. The x or horizontal axis can have any distribution, since we always run regression on y conditional on x values (the x values are treated as constants). On correlation , when data is normally distributed on both axis, the correlation coefficient is a fundamental parameter of the data. But one could measure and talk about correlation coefficient for non normal data without any issues at all.

Faithalone

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I had it backwards - you're right. If you leave a comparison for the assumption of normality for correlation and regression, I'll accept the answer. I apologize for the confusion.

Cmartman

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Could you extend the time?

Faithalone

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I just extended it.