Correlation and Bivariate Regression in Practice

Answer

Correlation and Bivariate Regression: Case Study

Correlation enables determination of whether measurement variables have an association and quantify the strength or degree of the relationship between the variables. Regression, on the other hand, expresses the association in form of an equation. Bivariate regression is an extensive examination of the effects of an independent variable on the dependent variable, while also exploring the form or nature of the relationship (Cohen, 2010). The method of least squares enables exploitation of relationship in choosing and fitting appropriate model. Johnson and Kuby (2011) cite assumptions that regulate the use of regression and correlation as: observations are independent, variables are random (not necessary for the independent variable in bivariate regression), response variable should follow a normal distribution when testing hypothesis. This discourse is an articulate assessment of the use of correlation and bivariate regression in a research work by Fang Wang, Lin Wang and Yuming Chen reported in the article “A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities” (Wang, Wang, & Chen, 2018).

Case Study

This research study was hugely influenced by the increasing dominance of air pollution in recent years, further anchored by the World Health Organization’s 2016 confirmation that 92% of the world populace live in niches with beyond limit air quality. While governments have set strategies for fighting air pollution, this study’s concern on the relationships of variables involved is abstracted to aid in management of the menace. The study proposed a new bivariate linear regression model based on detrended fluctuation analysis (DFA). The model provides estimators of multi-scale regression coefficients to measure association and dependence between variables. The focus is on three northern china cities (Beijing, Tianjin, and Baoding) as the PM2.5 for these cities are analyzed. The study reports that “The estimated regression coefficients confirmed the dependence of PM2.5 among the three cities and illustrated that each city has different influence on the others at different seasons and at different time scales” (p.1). The study employed the use of bivariate regression to investigate the dependence of the PM2.5 variable across the three cities. This was because the use of these methods of statistical analysis was cited as the most appropriate since they examined degree of linear relationships of variables across the three adjacent cities.

Assessment

The bivariate linear regression used was the most appropriate statistic for determining the variable relation across the cities. However, to investigate variable relationships, correlation static is a primal anchorage to which bivariate regression attests the nature of association. Being the simplest and most sufficient quantitative analysis form that can be utilized to measure linear relationships between predictor and response variables, correlation and bivariate linear egression are the most appropriate statistical analysis forms for assessing the empirical association of the variables under study. The study itself rimes bivariate regression as “the simplest and most mature method to describe the dependence of variables” (p.2).

The authors of this article diaplyed the research data for both correlation and bivariate regression.

Table 1: Correlation coefficients across cities in four complete seasons.

The results table here stands alone since the correlation coefficients are evidentially indicated and can be directly interpreted to ascertain association. Correlation coefficients are, in this case, not used to test any hypothesis nor was hypothesis correlation tested based on significance in the study but rather the study was geared towards determining association of variables across cities in this stage of the research, subject to formulation of respective regression models in which the nature of variable collinearity and relationship is determined.

However, to assess the nature of the linear relationships, bivariate regression plots were displayed instead of tables to explain the relationship of the variables under question. The graphical sketches displayed regression coefficients and their standard deviations.

This study, beyond the expected determination of nature of linear relationships, used bivariate regression to investigate the dependency between independent and dependent variable in a very intricate sense, yet helpful was the statistical technique. Therefore, correlation and bivariate regression were sufficiently utilized in this research study to ascertain a socially helpful finding in terms of air pollution.