This paper examines how to effectively communicate the results of a multiple regression analysis, drawing on Kuiper's (2008) framework for presenting regression findings. It outlines the goals of multiple regression — description, prediction, and confirmation — and identifies the standard elements that should appear in a regression results table. Using a practical case study involving XYZ Corporation, the paper demonstrates how intelligence scores and extroversion scores can be used as bivariate predictors of weekly sales performance. The paper also addresses the role of tables, charts, and figures in presenting statistical findings, and discusses common pitfalls such as data misrepresentation and misleading extrapolation.
This report examines the communication of the results of a multiple regression analysis. Multiple regression is described both in theory and in applied form, demonstrating the progression of such an analysis. The multiple regression in this study examines bivariate factors — specifically intelligence and extroversion — in predicting the sales success of employees at XYZ Corporation.
According to multiple regression analysis as discussed by Kuiper (2008), the goals of multiple regression are threefold: (1) describe, or develop a model that captures the relationship between explanatory variables and a response variable; (2) predict, or use a set of sample data to make forecasts; and (3) confirm, in that theories are often developed about individual variables, including confirmation of which variables or combination of variables should be included in the model. Regression is then used to determine whether the contribution of each explanatory variable captures much of the variability in the response variable (Kuiper, 2008).
Standard information to report in a multiple regression table includes the following:
(1) Dependent variable; (2) Explanatory variables; (3) Estimates for the constant term and coefficient estimates for explanatory variables; (4) Standard errors for the estimates above; (5) Indication of which variables are statistically significant; (6) R-squared; and (7) Number of observations and sample period (Kuiper, 2008, p. 1).
The techniques used to present regression results depend on the nature of the analysis. Tables are commonly employed and are reported as serving a four-fold purpose:
(1) Exploratory function: Data can contain answers to questions that may be implicit in the viewer's mind. (2) Communication function: Once data are explored, they can be displayed to communicate what has been discovered. Tables provide data in a condensed, easier-to-understand form. (3) Storage function: Data are expensive to gather, and summarization of data serves as a precaution against data loss. Tables also enable the replication of statistical analyses by others and allow data to be transferred in aggregate form. (4) Decorative function: Tables are used to invite the participation of the reader (Kuiper, 2008, p. 1).
Due to the complexity of multiple regression analysis, there is no single accepted form for the presentation of results. Charts, graphs, and figures are less common in published social science research, partly because they are more expensive to publish. However, graphs, figures, and charts remain effective methods of data presentation when used appropriately.
There are two potential problems to avoid when using figures. First, figures should not misrepresent data by ignoring important data features. Second, when data are presented in a manner that invites extrapolation, it is not feasible for a group of scholars to accurately comprehend the intended message, and distortion can result (Kuiper, 2008, p. 1).
"XYZ Corporation salesperson prediction dataset and model"
The multiple regression reported in this study examined the bivariate predictors of extroversion and intelligence to determine which salespeople would be most successful at the company's new location. Salespeople with higher levels of intelligence and higher levels of extroversion were found to be the most successful performers at XYZ Corporation, and are therefore most likely to succeed in selling products at its new retail outlet. This analysis illustrates the practical value of regression-based prediction models in human resources and workforce planning contexts.
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