In regression the dependent variable is known as the response variable or in simpler terms the regressed variable.
The independent variable is called the Explanatory variable (or better known as the predictor) - the variable which influences or predicts the values. i.e. if the explanatory variable changes then it affects the response variable.
If we look at the equation: Y= α+ßX
Here Y is the Dependent variable or response variable.
X is the independent variable or the explanatory variable.
As the value of X changes, the value of Y will change
α and ß are constant here.
To remember easily you can think that X '' EXPLAINS '' how the value of Y will go and hence its the EXPLANATORY VARIABLE.