University of West Florida

Multiple Non-Linear Regression Analysis

Markus Schief

Table of Contents

I. Introduction and Purpose of this Project ... 3

II. Project Related Basics in Statistic s ... 4

III. Description of Selected Data Set ... 6

A. General Description ... 6
B. Boxplot ... 8
C. Histogram ... 9
D. Scatter Diagrams ... 10
E. Seasonal Index ... 11
F. Multicollinearity ... 12

IV. Regression Analyses ... 13

A. Simple Linear Regression Analysis ... 13
B. Multiple Regression Analysis – Linear Model ... 16
C. Analysis of Residuals ... 18
D. Multiple Regression Analysis – Natural Log Transformation ... 20

V. Prediction ... 21

VI. Conclusion ... 24

VII. References ... 26

VIII. Appendix ... 27

Introduction and Purpose of this Project

Statistical analyses are very important today. In many areas like science or economics, for example, statistical analyses are used to support assumptions and to predict future data. With regards to business administration, modern business statistics can be used to influence decision making in finance, marketing or production, for instance.
The scope of the current project is to analyze a data set “Ibell” of phone calls and to predict future quantity of phone calls based on a regression analysis. The “Ibell” data set is related to the U.S. based company International Bell Communications (Ibell) that owns and operates direct routes through-out the world (International Bell Communications, 2008). Four variables are provided in the “Ibell” data set; three independent variables and one dependent (also called response) variable. The independent respectively predictor variables are “Quarter”, “Price” (price charged for long-distance calls in US$), and “Perinc” (reflecting the local average personal income in US$). The dependent variable is “Quantity” – the number of long-distance phone calls. The present data set was provided by the professor of the QMB class. Thus, the data has not been personally collected and hence the author of this report can not personally guarantee for the quality of the data set. However, the predictor variables of “Quarter”, “Price”, and “Perinc” seem fairly reasonable influences on the number of long-distance calls, in general. There are three major parts in this report. First, a general description of the data set will be presented, including the sort of variables, the characteristics of the observations, and the peculiarities in the distribution. Second, regression analyses estimate the validity of a modeled relationship between the dependent and the independent variables. Finally, the researcher will predict future quantity of long-distance calls for the upcoming four quarters in order to support International Bell Communications in network capacity planning as well as in revenue forecasts, for instance.

Project Related Basics in Statistics

Since the current data set is only a sample of a population some crucial properties of sample statistics have to be taken into account before starting with the report. Every sample statistic has got a “sample” error, which is the result of the fact that the sample represents “only” an extract of the total population. Besides those inherent sampling errors, there are also nonsampling errors such as measurement errors, mismatch between sample and population, or experimenter bias, for instance (Gayle Baugh lecture notes). As previously mentioned, the researcher did not personally collect the data and therefore can only assume that non-sampling errors are not included in the data set.
Assuming a perfect sample data set, certain predictions on the total population are statistically valid. Although the sample coefficients are not the same as the population parameters, the distribution of latter parameters can be hence inferred from the sample. If the sample size is large enough (according to Anderson, Sweeny, Williams a size of 30 respectively 50 if population is highly skewed) the sampling distribution of a variable can be approximated by a normal distribution (Central Limit Theorem). In addition, the bigger the sample, the higher the probability that the sample result is relevant for the population. Thus, the higher the probability that the sample mean falls within a specified distance of the population mean (Anderson, Sweeney, Williams, 2006). However, “because a point estimator cannot be expected to provide the exact value of the population parameter, an interval estimate is often computed by adding and subtracting a value, called the margin of error, to the point estimate.” (Anderson, Sweeney, Williams, 2006, p. 307)

[...]