Correlation and Regression Analysis

Introduction

This research will attempt to answer the question: ‘What combination of personal attributes, i.e. enthusiasm, integrity, toughness, confidence, fairness, warmth, humility, and industriousness, best predicts effective leadership or mentorship?’ Correlation and regression analyses will be used in the study to establish the relationship between the independent and the dependent variables. Correlation tests are applied to show a relationship between these variables, which do not accommodate the assumption that the variables are dependent.

Correlation analyses show or dispute interdependence between two variables, an independent and a dependent one. There are three types of relationships expected in these analyses types. The first one involves a decrease in one variable when the other variable increases. The second one is shown when both variables increase simultaneously. The third relationship reflects no correlation between two variables (r=0.0).

Regression analyses are used to describe how a dependent variable is controlled by an explanatory variable. These tests assume that there is a causal effect to the response variable. However, there are advanced approaches to describe non-dependence relationships (Pagano, 2011). Correlation and regression analyses relate to this research question because several independent variables tend to predict one dependent variable (Jackson, 2012).

The independent variables are the personal attributes (enthusiasm, integrity, toughness, confidence, fairness, warmth, humility, and industriousness) that will be correlated with the dependent variable (effective leadership or mentorship). The aim of this study is to assess the relationship between the independent variables and the dependent variable. It, however, will not focus on determining the causal effect of the independent variables on the dependent variable. In fact, the research question does not seem to infer causal relationship between the independent variables and the dependent variable.

Methods

This study will use 60 participants aged between 25 to 50 years who will be balanced between male and female participants to be accommodated in the research. The people taking part will be selected on the basis of their professional working background. Only the working people will be selected which will be necessary in answering the research question that attempts to examine the relationship between the independent variables and the dependent variable.

They will be chosen after their agreement to the terms and conditions of the study. For them to understand the process, the study leaders will explain the goals of the study and its major components. The participants will also be made aware of the research question to be answered at the end of the study. Moreover, study participants will be expected to remain in the study until it is completed. There will be no financial gain for being recruited to participate in the research. So, the participation will be voluntary.

This study will assess the relationship between the independent variables and the dependent variable as contained in the research question. Among the independent variables one should name enthusiasm, integrity, toughness, confidence, fairness, warmth, humility, and industriousness.

These are the personal attributes that are expected to affect the dependent variable, i.e. leadership or mentorship. This study will measure the kind of effect these independent variables produce on the variable that is dependent on them, for example, how a high level of fairness and integrity is related to leadership or mentorship and whether a tough leader is a good leader or mentor. All these and other questions will be answered by testing the two types of variables appropriately.

The independent variables describe some quality instead of quantitative or numerical attributes. Thus, they are known as categorical variables (Pagano, 2011). Other instances of categorical variables are colour, texture, and beauty. This study will use ordinal scale of measurement for the independent variables. So, the variables will be grouped into categories which can provide data ordered in a meaningful manner. It has been shown that categories of dependent variables are best described using ordinal data (Mertler & Vannatta, 2005).

The independent and dependent variables in this study are perfect to be applied in a correlation study. In an experimental study, an experimenter can easily manipulate the dependent variables. However, it would be challenging to manipulate any of the independent variables in this study. Experimental studies are often conducted in the laboratory or in the population, but the experimenter can influence the dependent variable at will.

In addition, correlation study achieves to demonstrate the relationship between them. It is known that there exist research data and theories which interpret the information collected from studies involving the two sets of data. Therefore, it is difficult to predict causality. The research question does not give a clue on whether there are other factors that contribute to the relationship between the two variables. In such cases, studies demonstrate that it is prudent to describe the relationship without attempting to infer causal relationships (Jackson, 2012; Mertler & Vannatta, 2005).

Results

Correlation and regression statistical analyses will be conducted in this study to demonstrate the relationship between the independent variables and the dependent variable. Correlation analysis is chosen because it shows the interdependence between two variables that are undergoing some changes. The relationship, expressed by correlation co-efficient (r) will be positive, negative or no relationship at all. Regression analysis is chosen because it is an efficient statistical test for describing the ratio between dependent variable and multiple independent variables by developing a regression equation. These two tests will give information in the form of values which will be interpreted to answer the research question.

Discussion

The correlation analysis to be used in this study assumes that data is sampled from a normal distribution. It is with such assumption that interpretation can be made on the confidence interval and the null hypothesis. The null hypothesis will be the following: ‘there is no correlation between the independent variables and the dependent variable’.

The research question suggests that there is a positive correlation between the personal attributes of a leader or mentor and effective mentorship or leadership. In other words, as the level of personal attributes of a leader increases so does the level of effective leadership. If this correlation is statistically significant, then it can be expected that the said personal attributes tend to predict effective leadership. It will imply that high levels of personal attributes will correspond to the same high levels of effective leadership. However, the research question does not prove causality between the independent variables and the dependent variable. Therefore, it will be difficult to tell whether the said personal attributes have a causal effect on effective leadership (Jackson, 2012).

The study findings will have practical applications and importance in the working environment. Managers and leaders will understand the relationship between the personal attributes studied in this research and effective leadership. The results will also act as a guide to aspire leaders and mentors in organizations worldwide.

References

Jackson, S. L. (2012). Research methods and statistics: A critical thinking approach (4th ed.). Belmont, CA: Wadsworth.

Mertler, C. A., & Vannatta, R. A. (2005). Advanced and multivariate statistical methods: Practical application and interpretation (3rd ed.). Los Angeles, CA: Pyrczak.

Pagano, R. R. (2011). Understanding statistics in the behavioral sciences. Stamford, CT: Cengage Learning.