Regression analysis is a modeling technique for analyzing the relationship between a continuous (real-valued) dependent variable Y and one or more independent variables X1, X2,...,Xk. (Regression analysis is a 'method' of determining and understanding any relationship between a dependent value and one or more independent values.) The goal in regression analysis is to identify a function that describes, as closely as possible, the relationship between these variables so that we can predict what value the dependent variable will assume given specific values for the independent variables. (The ultimate goal of regression analysis is to be able to predict the dependent variable, when given the independent variable values. In order to do this, a function must be established that reflects the relationship between the dependent variable and the independent variables.)

In any regression model, there is an element of systematic relationship between the dependent variable and the independent variables. This systematic relationship is represented by a mathematical function. However, there is also an element of unsystematic variance, also known as disturbance, in which the dependent variable fluctuates away from the function of the independent variables. In summary, the dependent variable is dependent upon the function of the independent variables AND a given tendency to fluctuate away from the function.

Because of the variance that occurs due to unsystematic disturbance, the best that regression can do is provide a 'probable' value for the dependent variable, given the independent variable values. Statistics are used to identify the probability distributions of the dependent variable, for different values of the independent variables. Measurements exist to inform how reliable, statisically speaking, a regression function predicts the independent variable value.

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