Does data need to be normally distributed for multiple regression?
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.
What does it signify if the residuals aren’t random or normal?
When the residuals are not normally distributed, then the hypothesis that they are a random dataset, takes the value NO. This means that in that case your (regression) model does not explain all trends in the dataset. Thus, your predictors technically mean different things at different levels of the dependent variable.
Is the y-variable normally distributed in regression?
I suppose that is the origin of people thinking that the y-variable should be normally distributed as an assumption for regression, but the y-data distribution in regression is not conditional, and that is not true. It is desirable for estimated residuals to be normally distributed, though even that is not a very strict requirement.
Are there assumptions on response variable to be normally distributed?
Note: Linear regression does not have assumptions on response variable to be normally distributed. Instead, it has assumptions on residual needs to be normally distributed (See Gauss-Markov theorem ).
Do you have to use normality assumption 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.
Can you do regression analysis with non normal data?
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.