For this Assignment, you will continue your practice as a critical consumer of research. You will critically evaluate a scholarly article related to correlation and bivariate regression.
Answer:
The two most crucial and widely used tools of statistical analysis is Correlation and Regression. Generally, regression analysis is used to compute the causal relationship between the dependent and independent variables whereas correlation analysis is applied in the case where no response variables are identified. In this paper, we focus on critical evaluation of an academic journal by A. Colin & Cameron, 2006 regarding correlation and regression.
We basically use correlation coefficient (r) to test whether there is any linear relationship and ranges from +1 to -1. If r is greater than 0 (i.e. positive) then it imply that if one variable increases the other will also increase and vice versa whereas if r is less than 0 (i.e. negative) then it imply that if one variable increases the other will decrease (inverse relationship) and vice versa. If r is equal to 0 then there is no correlation or linear relationship.
The statistical significance of the correlation analysis tells us whether the correlations reported are the result of any random sampling error. But correlation is appropriate only for quantifiable data, that is the data in which the numbers are meaningfully sorted. Hence one cannot use correlation approach to analyze categorical data like gender, favorite color etc. We must also keep in mind that correlation does not mean one variable cause change in other variable, it just gives the linear relationship between two variables.
In order to predict and explain the relationship among variables, we must not consider the variables in isolation. Bivariate regression allows us to explain, predict and control the relationship among variables under study. This analysis involves predicting one variable on the basis of the information on another variable. The regression model consists variables of two types namely, dependent and independent variable. The variable to be explained is called the dependent variable whereas the variables used to explain the dependent variable is called the independent variable. The bivariate regression considers only one independent variable and the variables should be quantitative in nature as categorical variables would not be able to explain this.
The regression results shows r square which gives the statistical measurement of the closeness of the data to the fitted regression line. It is referred to as the coefficient of determination. One should always keep in mind that it is not an indication of the adequacy of the regression model.
In this journal, the authors have taken the house price as their dependent variable and house size as their independent variable and used correlation and bivariate regression tools to analyze it. It is observed that house size has a significant impact on house price and value of R square (0.6175) implies that almost 62% of variation in house price can be explained by house size.
Though there is very less difference between correlation and bivariate regression but still it is found that bivariate regression gives more information than correlation. So we need to go through some crucial limitation of correlation and bivariate regression. Firstly, r and bivariate regression (least square regression) are not resistant to outliers and there may be many other variables that affects our dependant variable other than our independent variable and these variables need not a necessarily be linearly related. Secondly the problem of exploration and overfitting arises. Hence these things cannot be explained by our analysis.
References
Kapur, S.K. (2008). Elements Of Practical Statistics. 3rd ed. Oxford & IBH Publishing Company Pvt. Ltd.
Majumder, Amita (2012). Statistics And Development Issues. 1st ed. New Delhi: Mittal Publications.
Colin A. & Cameron J. (2006). Review of Bivariate Regression.
