Correlation and linear regression are frequently used to evaluate the degree of linear association between two variables and also to find the empirical relationship. However, violations of assumptions often give results which are not valid. High value of correlation coefficient is taken as degree of linearity between two variables and attempt is made to fit linear regression equation. However, linearity implies high correlation but the converse is not true. The paper describes with examples that concept of linearity is different from correlations, effect of violation of assumptions of correlations and linear regressions and suggests procedures to improve correlation between two variables which can be extended to multi variables.
KeywordsLinearity; Correlation coefficient; Standard error; Normal distribution; Generalized inverse
Published Date: 2023-04-25; Received Date: 2023-03-28
