Regression tutorial

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Tutorial for Multivariate (Regression) Analysis

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Overview

Multivariate analysis can be performed using single-level, multiple-level, and multiple-relationship analysis. A completely different executable computer package that is called DETECT/MR is provided as a part of the DETECT package for this type of analysis. In the simplest of terms one need only think about all the bivariate correlations in DETECT as replaced by multiple correlations (OLS). In this sense any of the analyses can be performed except for multiple-variable analysis because this approach assumes a regression equation best fits the data. The references at the end of this page provide examples of this type of analysis using single-level analysis and multiple-relationship analysis. In this tutorial, we provide two traditional analyses that focus on the bivariate correlations. These analyses suggest a regression equation of the following sort: Structure + Culture = Performance. Moreover they suggest a multiple-level analysis within conditions. The same program that is used in the bivariate multiple-relationship program for multiple levels is used in DETECT/MR and shows the same results as the bivariate correlations except that the correlation is the multiple correlation from the equation Structure + Culture =Performance.

Data Set B

Chapter 6 of the original manual describes the data set.
- Section 6.1 gives a description of a sample data set.
The actual data
- To download the data click on data set B, and save the page as text.

DETECT Program

DETECT/MR for Windows® uses windows to tell DETECT/MR what analyses to perform. All the windows available in DETECT/MR are the same as those described in the manual. There is a brief manual that explains how to use DETECT/MR. The actual programs generated by DETECT and DETECT/MR for windows for the three analyses are listed at the beginning of each of the outputs described below.

Click here to view the complete DETECT for Windows® manual.
Click here to see the DETECT/MR manual.

Output

Click here to see the actual output from the single-level, multiple-level and multiple-variable bivariate overall analysis of data set B.
Click here to see the actual output from the within-conditions single-level, multiple-level and multiple-variable bivariate analysis of data set B. This shows how to run four analyses in one program on one data set and is a multiple-relationship analysis.
Click here to see the actual output from the multivariate (multiple regression) analysis of Data set B for the equation Structure + Culture =Performance.

Interpretation

The original Chapter 6 from the manual shows how the output from the two traditional bivariate analysis is interpreted.
- Section 6.2 interprets the results for the overall analysis.
- Section 6.3 (1MB) interprets the results within the two conditions of interest.
The DETECT Interpretation Guide gives a more detailed description of the tables.
The interpretation of the multivariate output is the same as for the multiple relationship-analysis described in Chapter 6.

Wherever the interpretations in Chapter 6 indicate a need to look up a value, DETECT/MR for Windows® no longer requires it.

A selection of published studies with real data using multiple regression analysis

The mathematics of the multivariate analysis:
Schriesheim, C. (1995). Multivariate and moderated within-and between-entity analysis (WABA) using hierarchical linear multiple regression. Leadership Quarterly, 6, 1-18.

Illustrations of multivariate single-level analysis:

Schriesheim, C., Neider, L. and Scandura, T (1998). Delegation and leader-member exchange. Academy of Management Journal, 41, 298-318.
Schriesheim, C., Cogliser,C., and Neider, L. (1995). Is it "trustworthy." A multiple levels of analysis reexamination of an Ohio State leadership study. Leadership Quarterly, 6, 111-145.

Illustration of multivariate, single-level, multiple-relationship analysis:
Schriesheim, C., Castro, S., and Yammarino, F. (2000). Investigating Contingencies: An examination of the impact of span of supervision and upward contollingness on leader-member exchange using traditional and multivariate within- and between-entities analysis. Journal of Applied Psychology, 85, 659-677.

The multivariate output in this tutorial is an example of a multivariate, multiple-level, multiple-relationship analysis

A note about DETECT

DETECT's practical significance indicators ( such as Cohen's eta squared) are compatible with the report of the American Psychological Association Task Force on Statistical Significance that effect sizes should "always" be reported along with p values, and that "reporting and interpreting effect sizes in the context of previously reported effects is essential to good research" (p. 599)

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