Which of the following statements are true regarding the relationship between Correlation and Regression in statistical analysis?

A. A zero correlation implies that the regression line is horizontal and the regression coefficient is zero.
B. Regression can exist even in the absence of correlation if there is a deterministic relationship.
C. Correlation measures the strength and direction of a linear relationship; regression quantifies the cause-effect relationship.
D. The regression coefficient is always positive when correlation is positive, but not necessarily equal.
E. The value of regression coefficient lies between –1 and +1, just like correlation coefficient.

Choose the correct answer from the options given below:

Correct option is C

• Statement A is incorrect: A zero correlation implies no linear relationship, and the regression line may be horizontal only when Y is not dependent on X. However, in general, a zero correlation does not imply a zero regression coefficient unless it's proven that the slope is zero.

• Statement B is correct: Regression analysis can be applied even when the correlation is zero, especially if there is a functional/deterministic relationship (e.g., polynomial or non-linear).

• Statement C is correct: Correlation quantifies the degree of linear association, whereas regression goes further to quantify the change in the dependent variable due to the independent variable (cause-effect assumption).

• Statement D is correct: Regression coefficient will be positive when correlation is positive, but its value depends on the units of variables, so it’s not bound between –1 and +1 like correlation.

• Statement E is incorrect: Regression coefficients are not constrained between –1 and +1. They are sensitive to the scale of measurement, unlike correlation which is unit-free.

Thus, the correct answer is: B, C and D only.

Information Booster:

• Correlation coefficient (r) lies between –1 and +1 and shows the degree of linear relationship.

• Regression coefficients (slope values) measure how much Y changes with X and can be any real number depending on the scale.

• If r = 0, it means no linear correlation, but non-linear relationships can still exist.

• Correlation is symmetric: Correlation between X and Y is the same as Y and X.

• Regression is asymmetric: Regression of Y on X is not the same as X on Y.

• The square of correlation coefficient (r²) gives the coefficient of determination, i.e., the proportion of variation explained by regression.

Additional Knowledge:

• Option A (Zero correlation = horizontal regression line) – Incorrect. Zero correlation implies no linear trend, but the regression line is horizontal only when the dependent variable does not vary with the independent variable at all.

• Option E (Regression coefficient between –1 and +1) –  Incorrect. This is a common misconception. Regression coefficients are unit-dependent and not bounded, unlike the correlation coefficient.