• Entry
• Entries A-Z
• Subject index

### Multiple Regression: Block Analysis

Multiple regression represents an equation wherein a set of predictor variables is used to create a predicted value for a dependent variable. The mathematical elements, often described as ordinary least squares, are such that the goal of the equation is the generation of a model where the sum of the squared deviations are minimized between the observed and predicted values (the sum of the actual deviations should be zero). The process of creating a value that minimizes the sum of the deviations represents the assumptions of the normal curve for any process that involves estimation of a mean or a correlation. This process simply takes the same set of expectations and for a standardized equation operates using the following equation:

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

This equation indicates that the predicted ... • • • 