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:

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

This equation indicates that the predicted value of the standardized value of the dependent variable (Y) should be equal to the sum of each of the predictor variables (X) multiplied by a standardized regression coefficient (β). A standardized equation, unlike a raw equation, does not have an intercept or constant as part of the equation unlike most expected linear equations (y = mx + b). Compared to the linear equation, the term “m” which represents the slope of the equation the value “β” represents the weighting of the standardized variable.

Block analysis provides a means of using a hierarchical regression analysis to determine whether a set of variables entered as a block can increase the multiple correlation coefficient, R. Sets of blocks of variables can be entered in succession to determine the impact of variables in subsequent blocks improve prediction after accounting for the impact of the prior blocks. Under such circumstances, there is a direct connection to the use of covariates in an equation and the process and procedure should be compared to determine which procedure most closely matches the assumptions of the researcher.

This entry begins with a focus on the use of a single block in the analysis and the reasons and concerns for that procedure. A block analysis, in this case, enters all the variables into the equation and retains all the indicators as part of the final equation. The choice of a block approach indicates a need to make sure all indicator variables be retained in the model. The use of multiple blocks provides for a sequential set of steps in the analysis to determine whether, after the consideration of initial variables, there exists additional variability accounted for by the addition of the subsequent blocks. Block analysis is important in the context of communication research to the extent that it provides a means of handling some of the challenges associated with the lack of control one encounters in field investigations where there are naturally always multiple variables at work.