Let\u2019s see.<\/p>\n
One of the most common questions asked by a researcher who wants to analyse their data through a linear regression model is: must variables, both dependent and predictors, be distributed normally to have a correct model? So if they are not, should I normalize them through a transformation, for example the logarithmic one?<\/strong><\/p>\n The answer is no<\/strong>: the estimation method used in linear regression, ordinary least squares (OLS) method, doesn\u2019t not require the normality assumption.<\/p>\n 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.<\/p>\n The only test of normality that you will need to perform, after fitting your regression model, is that of the residuals<\/strong> (i.e. the difference between estimated by the regression and the observed values of the dataset).<\/p>\n How can you do it? Let your statistical program calculate the residuals and show their distribution<\/strong> (as if they were some variable).<\/p>\n Alternatively, you can build an ad hoc plot to test normality<\/strong> (for example a qq-plot).<\/p>\n If, on the other hand, you really want to use a more objective decision criterion, that is not based on the plot interpretation, then you can do a normality test (for example Shapiro-Wilk Test).<\/strong><\/p>\n Many statistical programs do almost all of this by default (for example SAS, via the PROC REG command).<\/p>\n However, there are at least a couple of reasons why you should take a look at the distribution of your “Y” and of all your “X”:<\/p>\n Thus, for very skewed variables it might be a good idea to transform the data to eliminate the harmful effects.<\/p>\n In summary: it is a good habit to check graphically the distributions of all variables, both dependent and independent.<\/p>\n If some of them are slightly skewed, keep them as they are.<\/p>\n On the other hand, highly skewed variables should be normalized before fitting the model.<\/p>\n After fitting the model, it is necessary to make sure that the residuals are distributed normally, to ascertain its technical correctness.<\/p><\/blockquote>\n I assume that you will check all other assumptions of linear regression then: linearity, homoscedasticity, absence of autocorrelation and multicollinearity.<\/p>\n Before concluding, one more thing to note: checking the normality of the residuals is necessary not only for estimating the regression coefficients, but also for calculating confidence intervals and p-values \u200b\u200bthat you will get in your output (which interests you in most cases).<\/p>\n","protected":false},"excerpt":{"rendered":"\n