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Does the Y variable need to be normally distributed?
The answer is no! The variable that is supposed to be normally distributed is just the prediction error. It is the deviation of the model prediction results from the real results. Y = Coefficient * X + Intercept + Prediction Error. Prediction error should follow a normal distribution with a mean of 0.
Does Y have to 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.
Is Y normally distributed?
In this case you can clearly fit Y using OLS (fitting to a quadratic function) but Y is not normal distributed (since it is related to a sum of variables in which one of them is a quadratic function of a normal distribution.
Why is error term normally distributed?
OLS Assumption 7: The error term is normally distributed (optional) OLS does not require that the error term follows a normal distribution to produce unbiased estimates with the minimum variance. If the residuals follow the straight line on this type of graph, they are normally distributed.
Why do we assume that Y is not normally distributed?
Thus you assume that u is not normally distributed, because this would result in normally distributed y. But when you compute the QQ-Normal plot there is evidence, that the residuals are normally distributed. Thus anyone can assume that the error term is normally distributed, although y is not.
Why is the normal distribution important in psychology?
Why is the normal distribution important? The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed.
What does it mean when the error term is normally distributed?
Thus anyone can assume that the error term is normally distributed, although y is not. So what does it mean, when the error term seems to be normally distributed, but y does not? It is reasonable for the residuals in a regression problem to be normally distributed, even though the response variable is not.
Which is the mirror image of a normal distribution?
A normal distribution has a bell-shaped curve and is symmetrical around its center, so the right side of the center is a mirror image of the left side. Most of the continuous data values in a normal distribution tend to cluster around the mean, and the further a value is from the mean, the less likely it is to occur.