Biostatistics series module 6: Correlation and linear regression

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are...

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Bibliographic Details
Published in:Indian journal of dermatology Vol. 61; no. 6; pp. 593 - 601
Main Authors: Hazra, Avijit, Gogtay, Nithya
Format: Journal Article
Language:English
Published: India Wolters Kluwer India Pvt. Ltd 01.11.2016
Medknow Publications and Media Pvt. Ltd
Medknow Publications & Media Pvt. Ltd
Medknow Publications & Media Pvt Ltd
Wolters Kluwer Medknow Publications
Subjects:
Agreements
Analysis
Biometry
Bland-Altman plot
Conflicts of interest
correlation
Correlation analysis
correlation coefficient
IJD
intraclass correlation coefficient
method of least squares
Module on Biostatistics and Research Methodology for the Dermatologist - Module Editor: Saumya Panda
Pearson′s r
point biserial correlation coefficient
regression
Regression analysis
Spearman′s rho
Statistics
Variables
India
method of least squares
Spearman′s rho
Pearson′s r
correlation
Bland-Altman plot
regression
intraclass correlation coefficient
point biserial correlation coefficient
correlation coefficient
Spearman's rho
Pearson's r
Bland–Altman plot
ISSN:0019-5154, 1998-3611, 1998-3611
Online Access:Get full text
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Summary:Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson′s correlation coefficient (r). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman′s rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P < 0.05. A 95% confidence interval of the correlation coefficient can also be calculated for an idea of the correlation in the population. The value r2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation (y = a + bx), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.
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ISSN:0019-5154
1998-3611
1998-3611
DOI:10.4103/0019-5154.193662