It does not have to. It is simply a study where two variables have a joint probability density function. There is no requirement for both variables to be dependent - one may be dependent on the other (which is independent).
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The F-variate, named after the statistician Ronald Fisher, crops up in statistics in the analysis of variance (amongst other things). Suppose you have a bivariate normal distribution. You calculate the sums of squares of the dependent variable that can be explained by regression and a residual sum of squares. Under the null hypothesis that there is no linear regression between the two variables (of the bivariate distribution), the ratio of the regression sum of squares divided by the residual sum of squares is distributed as an F-variate. There is a lot more to it, but not something that is easy to explain in this manner - particularly when I do not know your knowledge level.
If there are only two variables, then the dependent variable has only one variable it can depend on so there is absolutely no point in calculating multiple regression. There are no other variables!
Dependent variable is the variable that can be measured. However, the independent variable is the variable that changes in the two groups.
An alternating function is a function in which the interchange of two independent variables changes the sign of the dependent variable.
Correlation is a measure of association between two variables and the variables are not designated as dependent or independent. Simple regression is used to examine the relationship between one dependent and one independent variable. It goes beyond correlation by adding prediction capabilities.