Computational Approach - The Regression Equation
A line in a two-dimensional or two-variable space is defined by the equation Y=a+b*X; in full text, the Y variable can be expressed in terms of a constant (a) and a slope (b) times the X variable. The constant is also referred to as the intercept, and the slope as the regression coefficient or B coefficient. For example, GPA may best be predicted as 1+.02*IQ. Thus, knowing that a student has an IQ of 130 would lead us to predict that his or her GPA would be 3.6 (since, 1+.02*130=3.6). In the multivariate case, when there is more than one independent variable, the regression line cannot be visualized in the two dimensional space, but can be computed just as easily (via Multiple Regression; the computations are actually quite complex). For example, if in addition to IQ we had other predictors of achievement (e.g., motivation, self-discipline) we could construct a linear equation containing all those variables. In general then, multiple regression procedures will estimate a linear equation of the form:
Y=a+b1*X1+b2*X2+...+bp*Xp