Those words connote causality, but regression can work the other way round too (use Y to predict X). The independent/dependent variable language merely specifies how one thing depends on the other. Generally speaking it makes more sense to use correlation rather than regression if there is no causal relationship.
Consider the following figure from Faraway's Linear Models with R (2005, p. 59). The first plot seems to indicate that the residuals and the fitted values are uncorrelated, as they should be in a
I was just wondering why regression problems are called "regression" problems. What is the story behind the name? One definition for regression: "Relapse to a less perfect or developed state."
Note that one perspective on the relationship between regression & correlation can be discerned from my answer here: What is the difference between doing linear regression on y with x versus x with y?.
This is because any regression coefficients involving the original variable - whether it is the dependent or the independent variable - will have a percentage point change interpretation.
I am doing multiple linear regression. I have 21 observations and 5 variables. My aim is just finding the relation between variables Is my data set enough to do multiple regression? The t-test result
There are four principal assumptions which justify the use of linear regression models for purposes of inference or prediction: (i) linearity and additivity of the relationship between dependent and independent variables: (a) The expected value of dependent variable is a straight-line function of each independent variable, holding the others fixed.
How does linear regression use this assumption? As any regression, the linear model (=regression with normal error) searches for the parameters that optimize the likelihood for the given distributional assumption. See here for an example of an explicit calculation of the likelihood for a linear model.
I would like to note that the question concerned the standard errors of the regression coefficients and not the values of the coefficients themselves. The above answer is misleading in this case.
I'm very confused about if it's legitimate to include a lagged dependent variable into a regression model. Basically I think if this model focuses on the relationship between the change in Y and ot...
