Regression Analysis and Variables

Correlation and Regression

The ability to evaluate the essential general assumptions underlying statistical models and to distinguish the concepts and techniques of regression analysis is important for scholarly research. This is a more important element for a doctoral learner focused on quantitative research in order to generate appropriate and credible conclusions. Interpreting types of variables, design frameworks, and treatments in statistical regression analysis is also an essential skill for upcoming research projects. An evaluation of general assumptions that underscore a statistical model has significant impacts on the validity or outcomes of the research data.

Essential Assumptions in a Statistical Model

Since statistical models are basically used as tools for conducting a study, they are based on some general assumptions. While these assumptions vary depending on the kind of research being carried out, there are common assumptions across statistical models. The first assumption underlying a statistical model is the belief that the model is correct. Generally most statistics are based on the assumption that the utilized model is correct for the study. This assumption can be assessed using a Fit Model platform that examines various factors of the model in relation to whether they are fit for the study. The other assumptions includes assumptions that variables are normally distributed, assumption of a linear relationship between dependent and independent variables, assumption of homoscedasticity, and assumption that variables are measured reliably (Osborne & Waters, 2002).

The assumption that variables are normally distributed can be assessed visual inspection of data plots and tests that provide inferential statistics on normality. The assumption of a relationship between dependent and independent variables can be evaluated through examining residual plots, conducting regression analysis that include curvilinear components or using previous research or theory to guide current analysis. The assumption of homoscedasticity can be evaluated through a visual examination of a plot of the standardized residuals. The assumption that variables are measured reliably can be assessed using simple regression.

It's important to assess the assumptions that underlie a statistical model because of their probable impact on validity or outcomes of the research data. Assumptions affect outcomes or validity of the research data through generating Type I or Type II errors when conducting the analysis. In some cases, these assumptions contribute to under- or over-estimation of effect sizes or significance, which leads to serious biases and affect validity/outcomes of the research data.

Components/Concepts of Regression Analysis

Regression analysis is a statistical technique used to examine relationship between variables in order to determine the casual effect of one variable on another (Sykes, n.d.). There are four major components/concepts of regression analysis i.e. regression equation, P-values, R2/R-Squared, and residuals. Regression equation is the mathematical formula utilized in the explanatory variables to best estimate the dependent variable while P-value is the probability generated from the statistical test for the coefficients linked to every independent variable (Arcgis Resources, n.d.). R-Squared is a statistic obtained from the regression equation whereas residuals are the unexplained segments of the dependent variable. Regression equation is included in order to best determine the dependent variable being modeled while P-value helps in determining probabilities. On the other hand, R-Squared helps in interpretation of the model whereas residuals are used to develop and adjust the regression model.

Regression analysis is used over some other designs because it helps a researcher to explore and determine the casual impact of one variable over another through examine the relationship between variables. Researchers use this design over others in order to evaluate the statistical significance of the predicted relationship between variables. Some of the strengths of regression analysis include the fact that it generates outcomes that are clearly associated with the obtained measurement, it's explicitly linked to actual data, and it shows uncertainty through prediction or confidence levels. However, the limitations of this statistical tool include its unsuitability for tests that do not involve relationship between variables, it's based on assumption that the relationship between variables remains unchanged, and it incorporates complex and lengthy calculations and analysis.

There are two major types of regression analysis that have distinctive differences i.e. correlation/simple regression and multiple regression approaches. Simple regression involves using one independent variable to determine the value of a dependent variable while multiple regression approach entails using two or more independent variables to determine the value of an independent variable. Therefore, the level of measurement in simple regression is the use of a single independent variable while multiple regression measures two or more independent variables. With regards to analyzing and interpreting types of variables, single regression is based on the idea that a response variable does not vary based on independent variable while multiple regression is based on the concept that a response variable differs across different independent/explanatory variables (Sykes, n.d.). This implies that the criteria needed for the use of these approaches is based on the number of independent variables i.e. correlation is used when there is a single independent variable while regression is used if there are two or more independent variables. Statistical tests that are suitable for correlation approach include Chi Square tests and t-Test while those suitable for regression are ANOVA, ANCOVA, and MANOVA tests.