Question

Which of the following takes the value from -1 to 1?

• A. Correlation co-efficient
• B. Regression co-efficient
• C. Probability
• D. Fisher and Yates coefficient

Hint:

Statistical Metric Limits:
Correlation Coefficient ($r$) $\rightarrow -1 \le r \le +1$.
Probability ($P$) $\rightarrow 0 \le P \le 1$.
Regression Coefficient ($b$) $\rightarrow -\infty \le b \le +\infty$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Mathematical bounds of statistical metrics: Pearson's product-moment correlation coefficient ($r$) is bounded strictly between $-1$ and $+1$ ($-1 \le r \le +1$).
Key Formula or Approach:
\[ -1 \le r \le +1 \quad \mid \quad 0 \le P(E) \le 1 \quad \mid \quad -\infty < b < +\infty \]

Step 2: Detailed Explanation:
Evaluating mathematical boundaries of statistical parameters:
1. Correlation Coefficient (r) (A): Standardized dimensionless covariance measuring the strength and direction of linear association between two continuous variables; bounded strictly between $-1.0$ and $+1.0$ ($-1 \le r \le +1$).
2. Regression Coefficient (b): Slope of regression line; ranges from $-\infty$ to $+\infty$.
3. Probability (P): Bounded between $0$ and $1$ ($0 \le P \le 1$, cannot be negative).

Step 3: Final Answer:
Hence, Correlation co-efficient takes the value from -1 to 1, corresponding to option (A).