QUANTITATIVE METHODS

Quantitative Methods

Quantitative Methods

Introduction

A model is an idealized, abstract, and structured representation of real phenomena. Models may manifest as verbal descriptions, physical objects, diagrams, maps, mathematical formulas, and computer programs. Representation of complex dynamic systems increasingly involves computer simulation of alternative model outcomes based on specified input parameters, variables, and relationships.

The purpose of this paper is to find out the parsimonious model for the data set provided; Beatrice would like to construct a model to relate her advertising efforts with her daily sales for the next day. The principle of parsimony is that models should be as simple as possible but no simpler. One way to assess parsimony is to measure the number of elements and relationships therein. Models with fewer interacting elements have more explanatory power than models that emphasize detail and complexity over dynamic essence. Model utility is also revealed by its relative transparency: Can the model be understood by a broad audience? Are the feedback mechanisms driving system behavior clearly documented? Models that lack transparency have a limited utility beyond the experts who interact with them.

Discussion

The authenticity of a model may be assessed in multiple ways—by comparing simulated results with empirical observations and testing whether the model is consistent with the hypothesis articulated a priori. While no model will fully represent reality, modelers and decision makers will assess how plausible the model results seem on the basis of their prior assumptions about the system of concern. Because models are abstractions of reality, regardless of how intricate, much insight may be gleaned from parsimony, the art of leaving things out.

These models link a system's structure to behavior for the purpose of changing a structure to improve behavior. The purpose of a model provides the basis on which its utility must be judged, as all models are by definition simplifications of reality. This entry discusses the modeling process, the assessment of model utility, and the differences among several common modeling paradigms.

Methodology

To do this, she has collected data from the last two years of business. For each day, she has noted how much she spent for print advertising and whether or not she had an advertisement place on the website of The Vancouver Sun. Additionally, she has recorded her sales for the next business day.

For this data set, we have selected the multiple linear regression models. Multiple regressions are a general and flexible statistical method for analyzing associations between two or more independent variables and a single dependent variable. As a general statistical technique, multiple regressions can be employed to predict values of a particular variable based on knowledge of its association with known values of other variables, and it can be used to test scientific hypotheses about whether and to what extent certain independent variables explain variation in a dependent variable of interest.

As a flexible statistical method, multiple regressions can be used to test associations among continuous as well as categorical variables, and it can be used to test associations between individual independent variables ...