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### Multiple Regression: Multiple R

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

$\begin{array}{l}\mathrm{Predicted}\phantom{\rule{0.25em}{0ex}}\mathrm{value}\phantom{\rule{0.25em}{0ex}}\mathrm{of}\phantom{\rule{0.25em}{0ex}}Y=\\ {\mathrm{\beta }}_{1}{X}_{1}+{\mathrm{\beta }}_{2}{X}_{2}+{\mathrm{\beta }}_{3}{X}_{3}+\cdots +{\mathrm{\beta }}_{i}{X}_{i}.\end{array}$

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) ... • • • 