Probability & Statistics/Linear regression

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Question
hi,

I am of the understanding that Linear regression is used to predict, (extrapolate?) the dependent variable (y) from the independnt (x) by obtaining the relationship betweeen the two. Will it work however, if the (y) dependent variable is non normally distributed and the (x) independent variable displays a normal distribution, or do they both need to be normally distributed?

Answer
When a linear regression indicates that two variables (x and y) are likely to be related, this means they have a linear relationship like y = mx+b. If either one of them is normally distributed, so is the other, because any linear combination of normally distributed random variables will be itself normally distributed.

So if one of your variables (say, x) is known or very likely to be normal, and you have a strong correlation on your linear regression, then the other one (y) is very likely to be normal.

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Clyde Oliver

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I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

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I am a PhD educated mathematician working in research at a major university.

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Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

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BA mathematics & physics, PhD mathematics from a top 20 US school.

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Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

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In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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