Multiple Regression: Multiple R

Multiple regression is the process of generating an equation using a combination of predictor [Page 1051]variables to create an expected outcome. The equation appears as follows:

$$\begin{array}{l}\mathrm{Predicted}\mathrm{value}\mathrm{of}Y=\\ {\mathrm{\beta }}_1{X}_1+{\mathrm{\beta }}_2{X}_2+{\mathrm{\beta }}_3{X}_3+\cdots +{\mathrm{\beta }}_i{X}_i.\end{array}$$

The equation is true where the β represents the standardized coefficient for each variable X (this is in pairs so that each variable X has a separately estimated coefficient, β). The process involves the use of a combination of predictor variables (X) to estimate an outcome (the Y variable). This equation is considered a standard equation where the expression has been adjusted to remove the scale metric and does not use the raw weights (b). The prediction is based on the value using a z score estimate for each variable in the analysis (X and Y). Each coefficient used (βi) provides the unique contribution for each variable (removing the influence of the other variables in the equation). Unlike a raw equation, the standardized equation has no intercept (constant) because the constant is subtracted (and coefficients standardized) and the values go through the origin.