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.
Table of Contents
I. Introduction and Purpose of this Project
II. Project Related Basics in Statistics
III. Description of Selected Data Set
A. General Description
B. Boxplot
C. Histogram
D. Scatter Diagrams
E. Seasonal Index
F. Multicollinearity
IV. Regression Analyses
A. Simple Linear Regression Analysis
B. Multiple Regression Analysis – Linear Model
C. Analysis of Residuals
D. Multiple Regression Analysis – Natural Log Transformation
V. Prediction
VI. Conclusion
Research Objective and Key Themes
The primary objective of this report is to analyze the "Ibell" data set, consisting of 76 observations, to predict the future quantity of long-distance phone calls for the upcoming four quarters. By evaluating various regression models, the research seeks to establish a valid relationship between the dependent variable "Quantity" and the independent predictor variables "Quarter" and "Perinc" to support business decision-making in network capacity planning and revenue forecasting.
- Statistical data description and distribution analysis
- Application of simple and multiple linear regression models
- Testing for multicollinearity, heteroscedasticity, and autocorrelation
- Use of natural log transformation to improve regression model fit
- Predictive modeling using moving average and exponential smoothing approaches
Excerpt from the Book
Description of Selected Data Set
The following chapter deals with a description of the data set “Ibell”. Starting with a general presentation of some data properties of the corresponding data set, there will be additional graphical illustrations of the data set. For instance, a box plot, a histogram, a seasonal index, and some scatter diagrams will be presented in order to run a first step description and analysis of the “Ibell” data set. The main focus will be on the dependent variable “Quantity”.
General Description
The data set contains 76 observations – it is complete and not missing any information – and four variables – three independent and one dependent variable. All variables are based on quantitative data and they are measured in a ratio scale. “The scale of measurement for a variable is a ratio scale if the data have all the properties of interval data and the ratio of two values is meaningful.” (Anderson, Sweeney, Williams, 2006, p. 7) Moreover, the data set comprises time series data which means that the observations were collected over several time periods. With respect to the source of the data the researcher can only make assumptions since the data was not personally collected. There is no denying the fact, that the variables “Quarter”, “Price”, and “Quantity” can be extracted from existing sources like company records, for instance. The fourth variable “Perinc”, however, is supposed to be derived from statistical studies.
Summary of Chapters
I. Introduction and Purpose of this Project: Outlines the scope of the project, which involves analyzing the "Ibell" data set to predict phone call volume, and defines the dependent and independent variables.
II. Project Related Basics in Statistics: Discusses fundamental statistical concepts such as sample versus population, hypothesis testing, alpha levels, and p-values to establish the theoretical basis for the project.
III. Description of Selected Data Set: Provides a comprehensive descriptive analysis of the data using various graphical tools, including boxplots, histograms, and scatter diagrams to ensure prerequisites for regression are met.
IV. Regression Analyses: Covers the step-by-step development of regression models, starting from simple linear regression to multiple linear regression and finally non-linear regression using natural log transformation.
V. Prediction: Details the application of the developed models to forecast future phone call quantities for the next four quarters using moving average and exponential smoothing for the input variable "Perinc".
VI. Conclusion: Summarizes the findings, acknowledges the limitations of the prediction models, and confirms the feasibility of using the non-linear regression model for business planning.
Keywords
Multiple Regression, Non-Linear Regression, Natural Log Transformation, Quantity, Quarter, Perinc, Heteroscedasticity, Multicollinearity, Prediction, Business Statistics, Forecasting, Statistical Inference, ANOVA, Mean Absolute Percentage Error, Data Analysis
Frequently Asked Questions
What is the primary focus of this research?
The paper focuses on analyzing the "Ibell" data set to accurately predict the future volume of long-distance phone calls by identifying significant relationships between variables.
What are the key independent variables used in this study?
The study utilizes "Quarter" (time) and "Perinc" (local average personal income) as the core predictors for the dependent variable "Quantity".
What is the main goal of the regression analysis?
The goal is to develop a reliable statistical model that provides the best fit for the data, allowing for precise revenue and capacity planning predictions.
Which scientific method is employed to reach the conclusions?
The author employs quantitative statistical methods, including simple and multiple linear regression, residual analysis, and natural log transformations to optimize the model.
What does the regression model reveal about the data?
The analysis reveals strong positive correlations between the predictors and the call volume, while identifying and correcting for heteroscedasticity.
Which keywords best characterize this project?
Key terms include Multiple Regression, Forecasting, Heteroscedasticity, and Natural Log Transformation.
Why did the researcher choose to use a natural log transformation?
The transformation was applied to rectify heteroscedasticity issues identified in the residual plots, thereby creating a more accurate and robust non-linear prediction model.
How is the "Perinc" variable estimated for future periods?
Future values for "Perinc" were estimated using moving average and exponential smoothing techniques to account for missing statistical records for the upcoming quarters.
- Citar trabajo
- Markus Schief (Autor), 2008, Multiple Non-Linear Regression Analysis, Múnich, GRIN Verlag, https://www.grin.com/document/93742
