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Is it possible to have a (multiple) regression equation with two or more dependent variables Are there any special considerations for multilinear regression? Sure, you could run two separate regression equations, one for each dv, but that doesn't seem like it.

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Those words connote causality, but regression can work the other way round too (use y to predict x) What statistical tests or rules of thumb can be used as a basis for excluding outliers in linear regression analysis The independent/dependent variable language merely specifies how one thing depends on the other

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Generally speaking it makes more sense to use correlation rather than regression if there is no causal relationship.

Also, for ols regression, r^2 is the squared correlation between the predicted and the observed values Ridge regression is useful as a general shrinking of all coefficients together It is shrinking to reduce the variance and over fitting It relates to the prior believe that coefficient values shouldn't be too large (and these can become large in fitting when there is collinearity) lasso is useful as a shrinking of a selection of the coefficients.

A good residual vs fitted plot has three characteristics The residuals bounce randomly around the 0 line This suggests that the assumption that the relationship is linear is reasonable Consider the following figure from faraway's linear models with r (2005, p

The first plot seems to indicate that the residuals and the fitted values are uncorrelated, as they should be in a

In answering this question john christie suggested that the fit of logistic regression models should be assessed by evaluating the residuals I'm familiar with how to interpret residuals in ols, t. .in general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. The pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x)

This suggests that doing a linear regression of y given x or x given y should be the.