Are linear dependent data normal distributed?

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Homework Help Overview

The discussion revolves around the relationship between linear regression models and the normal distribution of data. Participants are exploring whether data that can be modeled using least squares regression is necessarily normally distributed.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants attempt to clarify if normally distributed data is a requirement for linear regression models, while others question the implications of non-normality on statistical significance testing.

Discussion Status

The discussion is ongoing, with some participants suggesting that data fitting a linear model does not have to be normally distributed, while others are uncertain about the implications of this on statistical methods. There is no explicit consensus yet.

Contextual Notes

Participants are considering the constraints of applying standard statistical tests to non-normally distributed data and the potential need for alternative methods.

Science4ver
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Homework Statement



Lets say we have some data which we using the method of the least squares regression can express a linear regression model.

I would like to know if this data generelly will be normal-distributed if it can be expressed by a linear regession model? and if so any way to explain the connection between normel distributed data and linear regression?
 
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Generally speaking, yes, the data is normal distributed.
Now on the second question: I'm not sure. I have to check that out.
 
Science4ver said:

Homework Statement



Lets say we have some data which we using the method of the least squares regression can express a linear regression model.

I would like to know if this data generelly will be normal-distributed if it can be expressed by a linear regession model? and if so any way to explain the connection between normel distributed data and linear regression?

No, not necessarily. Non-normally-distributed data can (and very often is) described by a linear regression model. The main problem with having non-normal data is that one cannot apply standard, textbook statistical tests of significance. (However, fancier methods are available to deal with these cases.)

RGV
 
So the generel answer to my question is No? Data which fits a liner model by the use of the least square method doesn't have to normal distributed.
 

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