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Should independent variables be normally distributed?
They do not need to be normally distributed or continuous. It is useful, however, to understand the distribution of predictor variables to find influential outliers or concentrated values. A highly skewed independent variable may be made more symmetric with a transformation.
What happens if the dependent variable is not normally distributed?
In short, when a dependent variable is not distributed normally, linear regression remains a statistically sound technique in studies of large sample sizes. Figure 2 provides appropriate sample sizes (i.e., >3000) where linear regression techniques still can be used even if normality assumption is violated.
What is an example of a normally distributed variable?
IQ scores and heights of adults are often cited as examples of normally distributed variables.
When does normally distributed and uncorrelated mean independent?
Normally distributed and uncorrelated does not imply independent. In probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables are normally distributed.
Are there any assumptions about the distribution of independent variables?
There are NO assumptions in any linear model about the distribution of the independent variables. Yes, you only get meaningful parameter estimates from nominal (unordered categories) or numerical (continuous or discrete) independent variables.
When do X and Y have a normal distribution?
To say that the pair (X, Y) of random variables has a bivariate normal distribution means that every constant (i.e. not random) linear combination aX + bY of X and Y has a univariate normal distribution. In that case, if X and Y are uncorrelated then they are independent.
How to find the distribution of a random variable?
If X 1, X 2, …, X n >are mutually independent normal random variables with means μ 1, μ 2, …, μ n and variances σ 1 2, σ 2 2, ⋯, σ n 2, then the linear combination: We’ll use the moment-generating function technique to find the distribution of Y.