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Should dependent variables be normally distributed in linear regression?
The answer is no: the estimation method used in linear regression, ordinary least squares (OLS) method, doesn’t not require the normality assumption. So, if you see that a variable is not distributed normally, don’t be upset and go ahead: it is absolutely useless trying to normalize everything.
What effect would non normality have on the regression model?
Regression only assumes normality for the outcome variable. Non-normality in the predictors MAY create a nonlinear relationship between them and the y, but that is a separate issue. You have a lot of skew which will likely produce heterogeneity of variance which is the bigger problem.
Can I use linear regression for non-normal data?
In linear regression, errors are assumed to follow a normal distribution with a mean of zero. It seems like it’s working totally fine even with non-normal errors. In fact, linear regression analysis works well, even with non-normal errors. But, the problem is with p-values for hypothesis testing.
Can regression be applied to non normal data?
In fact, linear regression analysis works well, even with non-normal errors. That means that in Case 2 we cannot apply hypothesis testing, which is based on a normal distribution (or related distributions, such as a t-distribution).
Do you need a dependent variable for linear regression?
To run a linear model, you don’t need an outcome variable Y that’s normally distributed. Instead, you need a dependent variable that is: The normality assumption is about the errors in the model, which have the same distribution as Y|X.
Which is an example of a dependent variable with no bounds?
A better example would have used a dependent variable that truly had no bounds. GPA isn’t one—it’s bounded at 4.0 at the top and 0 at the bottom. See #3 for why I got away with it anyway. SAT math score, a predictor, which is also bounded between 200 and 800, is irrelevant.
Do you have to use a normal distribution in a regression?
7 Answers 7. You don’t need to assume Normal distributions to do regression. Least squares regression is the BLUE estimator (Best Linear, Unbiased Estimator) regardless of the distributions. See the Gauss-Markov Theorem (e.g. wikipedia) A normal distribution is only used to show that the estimator is also the maximum likelihood estimator.
What kind of regression would be appropriate for continuous dependable variable?
Hi Karen, thank you for your many excellent posts. What kind of regression would be appropriate for a continuous dependable variable that has only a lower bound (zero) and no upper bound Unfortunately, it depends. Here are a few options, depending on how many 0s there are and the distribution.