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) ...