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Why is the assumption of a normally distributed residual relevant to a linear regression model? [duplicate]

Isn't it just the assumptions of autocorrelation, unbiasedness and homoscedasicty that are relevant to proving the efficiency and the unbiasedness of OLS estimators? How does the normality in the ...
182 views

Assumption of normally distributed residuals in linear regression [duplicate]

Let us consider the simple linear model $y = \beta_0 + \beta_1 X + \epsilon$, where $y$ is real number, $X$ a matrix of reals and $\epsilon$ is the random "noise". The least-square estimate of the ...
233 views

Why does the linear regression algorithm assume the input residuals (errors) to be normal distributed? [duplicate]

I am trying to know the assumptions of linear regression (LR). I understand linear regression needs the relationship between the independent and dependent variables to be linear, but LR also assumes ...
60 views

Why is Gaussian distribution used for Maximum Likelihood estimation with Linear Regression and not some other distribution? [duplicate]

Why is Gaussian distribution used for Maximum Likelihood estimation with Linear Regression and not some other distribution? I know that using Gaussian distribution for the target y yields Maximum ...
53 views

For linear regression, is it important for predictors and response to be normally distributed? [duplicate]

I get that for simple linear regression, say y=b0+b1*x + error, the errors should be normally distributed, have no autocorrelation, constant variance. I also understand that there should be no ...
36k views

What if residuals are normally distributed, but y is not?

I've got a weird question. Assume that you have a small sample where the dependent variable that you're going to analyze with a simple linear model is highly left skewed. Thus you assume that $u$ is ...
3k views

Why should we use t errors instead of normal errors?

In this blog post by Andrew Gelman, there is the following passage: The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian ...
42k views

Assumptions to derive OLS estimator

Can someone briefly explain for me, why each of the six assumptions is needed in order to compute the OLS estimator? I found only about multicollinearity—that if it exists we cannot invert (X'X) ...
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Why is the normality of residuals “barely important at all” for the purpose of estimating the regression line?

Gelman and Hill (2006) write on p46 that: The regression assumption that is generally least important is that the errors are normally distributed. In fact, for the purpose of estimating the ...
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Linear regression: any non-normal distribution giving identity of OLS and MLE?

This question is inspired from the long discussion in comments here: How does linear regression use the normal distribution? In the usual linear regression model, for simplicity here written with ...
2k views

Normality assumption in linear regression

As an assumption of linear regression, the normality of the distribution of the error is sometimes wrongly "extended" or interpreted as the need for normality of the y or x. Is it possible to ...
2k views

Linear regression and assumptions about response variable

Wikipedia states: Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a set of observed values ...
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Simulating data for linear regression

I am trying to simulate two data set for multiple linear regression. I want one data which is independent and identically distributed and the other is not. So far, I have done the following: ...
By OLS regression equation: $$Y = a + bX + e$$ My thoughts are that homoscedasticity by definition imply that $Var(Y|X) = Var(e|X)=$ constant, then this would imply that $Var(e|X) = Var(e)$ which ...
Estimating a function $f$ of a random vector $\mathbf{x}$ by a subset of the coordinates of $\mathbf{x}$ after a rotation of the input space
Suppose I have $$h=f(\mathbf{x})$$ with $f$ a deterministic function and $\mathbf{x}=(x_1,\ldots,x_n)$ a random vector of known distribution. I'm not using the capital letter notation for random ...