The presentation of a multiple regression analysis is addressed in the work of Kuiper (2008) that the goals of multiple regression analysis are to: (1) describe or develop a model that describes the relationship between the explanatory variables and the response variable; (2) predict or use a set of sample data to make predictions; and (3) confirm in that theories are reported as often developed about individual variables including confirmation of which variables or which combination of variables should be included in the model. Regression is then used to determine if the contribution of each explanatory variable in a model captures much of the variability in the response variable. (Kuiper, 2008)
Communicating the Results of a Multiple Regression Analysis
Business Theory: "Communicating the Results of a Multiple Regression Analysis"
This report has the stated objective of examining the communication of the results of a multiple regression analysis and as such, a multiple regression analysis is described both in theory and in form demonstrating the progression of such an analysis. The multiple regression in this study examines bivariate factors in predicting the success of sales people for XYZ corporation.
The presentation of a multiple regression analysis is addressed in the work of Kuiper (2008) that the goals of multiple regression analysis are to: (1) describe or develop a model that describes the relationship between the explanatory variables and the response variable; (2) predict or use a set of sample data to make predictions; and (3) confirm in that theories are reported as often developed about individual variables including confirmation of which variables or which combination of variables should be included in the model. Regression is then used to determine if the contribution of each explanatory variable in a model captures much of the variability in the response variable. (Kuiper, 2008) Standard information to report in a multiple regression table includes those stated as follows:
(1) Dependent variable;
(2) Explanatory variables;
(3) Estimates for constant term and coefficient estimates for explanatory variables;
(4) Standard errors for estimates above;
(5) Indication of which variables are statistically significant;
(6) R-squared; and (7) Number of observations/sample period. (Kuiper, 2008, p.1)
The techniques used are dependent upon the analysis. Many times tables are used. Tables are reported as having a four-fold purpose and specifically tables:
(1) Serve an exploratory function. Data can contain answer to questions that may be explicit in the viewer's mind.
(2) Tables have a communication function: once data are explored data can be displayed to communicate what has been discovered. Tables are reported to provide data in a form that is condensed and easier to understand;
(3) Tables serve a storage function: data are expensive to gather and summarization of the data serves as a precaution against data loss. IN addition, it is reported that tables enable the replication of statistical analyses by others and tables enable data to be transferred in aggregate form.
(4) Tables serve a decorative function: Tables are used to invite the participation of the reader. Due to multiple regression analysis complexity there is not an accepted form for presentation of results. Charts, graphs, and figures are much less common in social science research that is published due to the fact that it is expensive to publish these. However, use of graphs, figures, and charts to present data are all effective methods of data presentation. (Kuiper, 2008, p.1) There are two potential problems to avoid in the use of figures. First the figures should avoid the misrepresentation of data due to ignoring important data features. When data is presented in a manner that "invites extrapolation" this is not feasible for a group of scholars to attempt to comprehend and distortion occurs.
III. Multiple Regression Analysis Model and Analysis
The XYZ corporation is opening a new retail sales outlet and want to understand the best way to staff the stores with employees that will be best at selling their products. The staff sales are studied at stores already existing to examine the intelligence and outgoingness of employees so as to predict the sales performance of employees currently employed by the company. Three scores will be established for each salesperson including:
(1) Intelligence -- score on a scale of 50 (low intelligence) to 150 (high intelligence)
(2) Extroversion - score on a scale of 15 (low extroversion) to 30 (high extroversion)_
(3) Performance of sales expressed as the average total dollar of sales per week
The variables used to forecast are predictors and the variable is the criterion. The predictor and criterion data for the 20 current sales people of the XYZ company.
Sales Person
Intelligence
Extroversion
$ Sales/Week
1
89
21
2
93
24
3
91
21
4
23
5
27
6
18
7
98
19
8
16
9
23
10
28
11
20
12
25
13
20
14
26
15
97
28
16
29
17
25
18
88
23
19
19
20
16
These data can be analyzed through examining the bivariate or the: (1) correlation and the (2) bivariate regression equation of the sales vs. intelligence and sales vs. extroversion relationship. The results show that the bivariate correlation of r = .33 and the sales vs. extroversion of r = .55 are both positive.
Source: SABLE Virginia Tech (1997)
The bivariate analyses makes provision of a view of how well each of these predictors serves in the forecasting of performance of sales but is unable to demonstrate how the two predictors work together in the prediction of sales performance. The following shows how multiple regression is used to predict a criterion through use of two predictors:
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