Regression and ANOVA Methods: Theory and Examples Report

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Introduction

Regression Method

Description of the Technique and Purpose

Originally, there are several methods of quantitative analysis, and each had its own merits and demerits. Nevertheless, there are two methods which are regarded as the most widely used due to their relative simplicity and universality. Thus, regression method Generally refers to the application of the algorithms, which are intended for fitting compound and even arbitrary curves to one’s data using iterative judgment. (Maxwell, Delaney, 2007). According to Doyle (2003): “ Simple curves can be implemented in general linear models (GLM) and regression, and in models supported by the generalized linear modeling family (GZLM will implement logistic, profit, or gamma regression, among others, where the raw values of the dependent are nonlinearly related to the linear predictor (the terms on the right-hand side of the equation) because the dependent is transformed by some nonlinear link function)”.

Circumstances in which it is applied

This statistical technique is most commonly used in programme evaluation to estimate effects. The net effects of the programme under evaluation can be assessed using regression analysis, by attributing part of the changes observed to explanatory variables, while the remaining effects are attributed to the programme. For this reason, regression analysis is useful in ex-post evaluation, to determine the net impact of the programme. However, this technique can also be applied in forecasting and ex-ante evaluation.

Strengths

  • Regression analysis provides an opportunity to specify hypotheses concerning the nature of effects
  • When it is successfully executed, regression analysis can produce a quantitative estimate of net effects.

Limitations

  • The technique is demanding because it requires quantitative data relating to several thousand individuals.
  • Implementing the data collection can be time-consuming and expensive.
  • Relations between the different explained and explanatory variables are often circular (X explains Y and Y explains X). In this case, the method is inapplicable.

ANOVA Method

What is ANOVA? Basic Principles

ANOVA Method is grounded on two central arrogant: normality and equal variances. However, the practice shows that these arrogances are often violated. According to Newman and Benz (2003): “the studies of this method are generally concentrated on offering contemporary alternatives for one-way ANOVA test: these are mainly the trimmed methods one step M-estimators and bootstrap methods (a bootstrap-t method and a percentile method) with these two measures were used to compare groups based on comparing measures of location. Simulation studies were investigated according to four variables manipulated here: (a) six distribution shapes from the g-and-h distribution; (b) number of groups (4, and 6), (c) sample size, and (d) degree of variance heterogeneity.

Originally, for the successful analysis, ANOVA requires the following points to be observed:

  • Clear and distinct identification of the situation
  • Understanding of the assumptions for ANOVA and the stipulations where ANOVA test-statistics is robust
  • Writing the linear model for ANOVA and identifying the components of the model
  • Stating the null and alternative hypotheses for ANOVA method
  • Describing the partitioning of the general sum in ANOVA preparation part
  • Defining and computing SS total, SS groups, and SS within
  • Clarifying degrees of freedom and calculating mean-squares for various variability resources
  • Expand and interpret ANOVA tables and realize the relationships of the different parts of the matrix
  • Calculate and analyze the matrix statistic in one-way ANOVA
  • State the relationship between the data and matrix statistics (Myers, 2003).

Article 1

Objective

The paper is aimed to study and analyze the influence of dissimilarities between the International Financial Reporting Standards (IFRS) and Generally Accepted Accounting Principles in the United States (US GAAP) in the financial indexes of British corporations and firms. The main object of the paper is the Disclosure and harmonization of accounting standards has been the object of various studies the past few years. Financial Accounting Standard Board (FASB) and the International Accounting Standard Board (IASB) have made efforts towards bringing their respective standards into alignment, with the objective of eliminating asymmetries of information in relation to companies that operate in the American and European markets. (Beuren, Hein, 2008)

Introduction

The problems with information asymmetry were initially researched with the usage of Agency Theory, which is aimed to resolve the mentioned information asymmetry troubles and the consequences of these problems, as well as conflicts of interest between managers and organization shareholders. The structures of the corporate governance, besides allowing greater transparency and greater protection to minority shareholders, also seek to mitigate information asymmetry among various stakeholders in the organization. (Beuren, Hein, 2008)

In spite of the fact the information asymmetry created by resorting to various accounting norms from various countries does not depend on whether or not there are differences of interest between managers and shareholders, or on greater or less clearness in admission on the part of corporations.

Data (Implication and Empirical Models)

It is also emphasized that Organizations committed to the mechanisms of corporate governance need to make these distortions evident, thus guaranteeing clear information to every kind of investor, national or foreign. In this context, this paper intends to advance research on the subject, presenting a study on the impact provoked in economic-financial indicators of English companies with ADRs that publish AS in IFRS and US GAAP, by means of the differences between international and American accounting norms, starting with information sent by these companies to the London Stock Exchange (LSE) and the NYSE.

Results

Taking into account the connection to its approach to the issue, the research is featured as quantitative, and resorts to the Regression Method of quantitative research, which permits the compilation, in a set of constituents, information analogous between one element and another. Therefore, in applying it the existence of a set of more or less comparable elements is indispensable. (Beuren, Hein, 2008)

Robustness Analysis

First, assumptions with respect to the causality between leverage and agency problems can be tested. According to table 6 of the article it is shown that for underinvestment the regression coefficient of leverage appeared to be 0.01, with a t-value of 0.10.Our second robustness test involves the overinvestment problem. These findings show that managers are not persuaded through the governance structure to issue debt in order to reduce overinvestment

Conclusion

Finally, it should be emphasize that the idea of Regressive analysis may be widely applied towards the research of the business cases and the ideas of the quantitative research of structural and financial issues of the enterprises.

Article 2

Objective

The research reveals the effectiveness of regulatory principles by revealing the extent and quality of disclosures, completed in meeting the norms and requirements of the standard. Palmer (2008) emphasizes that the exploratory focus on the quality of disclosure demonstrates the role of AASB 1047 in helping users of financial statements to cope with the change; that is, the quality of what is being disclosed being just as important as the quantity of disclosure. However, it is generally accepted that accounting firms, and particularly the Big Four firms, develop so-called ‘boilerplate’ disclosures for clients to adopt in response to major new or amended disclosure requirements

Introduction

Research is aimed to study the Australian market in the long-term perspective, and finally it is aimed to find that turn of the month effect does exist in stock market.

Data and Methodology

The ANOVA model, which is used in this paper represents the fact, that sample AIFRS reports are available from some of the Big Four auditors. It is claimed that if it is the case that the companies are generally resorting to, they are using boilerplate discoveries to comply with AASB 1047. Thus, these discoveries do not accurately reflection of the impact of adopting AIFRS on the companies, or their preparedness for adoption. However, the disclosures reflect what the audit company distinguishes as the spheres where influences are likely to be the largest and the minimum required gathering the Australian Securities and Investments Commission’s approval.

Anova Model

General linear model procedure is used that can easily detect if TOM effect if found with OLS regression. The GLM is as follows:

The GLM
Figure 1. The GLM

Where RPeriod represents returns for the TOM and RMonth represents ROM period. According to table 5 of the article the F-test results across periods (TOM versus ROM) and show the null hypothesis is rejected for all five REIT indices at the one per cent significance level. This favours a TOM effect in all five indices REIT.

Conclusion

The research methods, which are used in both cases, represent different models of analyzing data. Regression method in Article 1 represents the linear analysis model. While ANOVA in Article 2, is essential for further research planning, and using the data in similar analyses and researches.

References

  1. Beuren, M. Hein, N (2008) “Impact of the IFRS and US-GAAP on economic-financial indicators” Managerial Auditing Journal, Vol. 23 No. 7, 2008, pp. 632-649
  2. Cohen, J., & Cohen, P. (1983). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
  3. Daymon, C., & Holloway, I. (2002). Qualitative Research Methods in Public Relations and Marketing Communications. London: Routledge.
  4. Doyle, A. M. (2003). Regression: A Universal Experience. Westport, CT: Praeger.
  5. MacPhee, D., Morgan, G. A., Gliner, J. A., & MacPhee, M. S. (2000). Research Methods in Applied Settings: An Integrated Approach to Design and Analysis. Mahwah, NJ: Lawrence Erlbaum Associates.
  6. Maxwell, S. E., & Delaney, H. D. (2007). Designing Experiments and Analyzing Data: A Model Comparison Perspective. Mahwah, NJ: Lawrence Erlbaum Associates.
  7. Maxwell, S. E., & Delaney, H. D. (2004). Designing Experiments and Analyzing Data: A Model Comparison Perspective. Mahwah, NJ: Lawrence Erlbaum Associates.
  8. Myers, J. L., & Well, A. D. (2003). Research Design and Statistical Analysis. Mahwah, NJ: Lawrence Erlbaum Associates.
  9. Newman, I., & Benz, C. R. (2003). Qualitative-Quantitative Research Methodology: Exploring the Interactive Continuum. Carbondale, IL: Southern Illinois University Press.
  10. Palmer, Ph. (2008) “Disclosure of the impacts of adopting Australian equivalents of International Financial Reporting Standards” Accounting and Finance 48, 2008, 847–870
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