# 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?

Ignore the nonsensical title.

What I'm really looking for is a comparison of the assumption for normality for correlation and regression.

• 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.

• 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.

• 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.

• 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.

• Could you extend the time?

• I just extended it.

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