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Regression techniques are used to find the best relationship between two or more variables. Here, best is defined according to some statistical criteria. The regression line is the straight line or curve based on this relationship. The relationship need not be a straight line - it could be a curve. For example, the regression between many common variables in physics will follow the "inverse square law".
Independent variable could be the number (or spacing or size) of the laces and the dependant variable is distance. Possibly levels of the independent variable could be ranges of number of laces.
The domain. It need not be the "independent variable" since the variables could be interdependent.
The three types of variables are: Independent: it is the one that you manipulate Dependent: the one that reacts to the changes in the independent variable and is measured in a experiment Control: all the other factors that could affect the dependent variable but are kept constant through out an experiment
Usually, yes. Obviously, only if you have one: the two variables could be inter-dependent.