Q.118
Read the following statements regarding Correlation and Regression
(A) . Correlation is a two-way relation whereas regression is a one-way relation
(B) . Correlation coefficient is dependent of units whereas regression coefficient is in the units of independent variate
(C) . The value of regression coefficient lies between -1 and +1
(D) . In the case of correlation one need to identify cause and effect. Whereas, in regression one need to know the cause but
not the effect
(B) . In the case of regression, one can predict the value of dependent variate for a given value of independent variate
Choose the correct answer from the options given below:
- Statistical Principles of Correlation and Regression:
- Statement (A) is correct: Correlation is a symmetric, two-way relationship between two variables ($r_{xy} = r_{yx}$), whereas regression is an asymmetric, one-way relationship where an independent variable ($X$) predicts a dependent variable ($Y$).
- Statement (E) is correct: The primary objective of regression modeling is to estimate and predict the value of the dependent variable ($Y$) for any designated value of the independent variable ($X$) using the regression equation $\hat{Y} = a + bX$.
- Statement (B) is incorrect: The correlation coefficient ($r$) is dimensionless (independent of units of measurement), whereas the regression coefficient ($b_{yx}$) is expressed in units of $Y$ per unit of $X$.
- Statement (C) is incorrect: While correlation $r$ lies strictly between $-1$ and $+1$, individual regression coefficients ($b$) can exceed $\pm 1$.
- Statement (D) is incorrect: Correlation does not imply cause-and-effect; regression assumes a directional functional dependency.
- Conclusion: Statements (A) and (E) are correct (Option 3).
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