AMU 2026 — Mathematics PYQ

Explanation:

Unlike the simple Pearson correlation coefficient ($r$), which ranges from $-1$ to $+1$ (indicating both direction and strength), the multiple correlation coefficient ($R$) is defined as the square root of the coefficient of determination ($R^2$).

Since $R^2$ represents the proportion of variance in the dependent variable explained by the independent variables, it must always be a non-negative value between $0$ and $1$. Consequently, the multiple correlation coefficient $R$ is defined to range from:

$$0\le R\le 1$$

Therefore, the minimum value that the multiple correlation coefficient can take is $0$, which indicates that there is no linear relationship between the dependent variable and the set of independent variables.

Would you like to explore how to calculate the multiple correlation coefficient for a specific dataset?