Question

Identify the correct formula for calculating r.

• A. $r=\frac{N\sum \left(X_i{Y}_i\right)–(\sum X_i)(\sum Y_i)}{\sqrt{N\sum X_i^2–(\sum X_i{)}^2}\sqrt{N\sum Y_i^2–(\sum Y_i{)}^2}}$
• B. $r=\frac{N\sum \left(X_i{Y}_i\right)–N(\sum X_i)(\sum Y_i)}{\sqrt{N\sum X_i^2–(\sum X_i{)}^2}\sqrt{N\sum Y_i^2–(\sum Y_i{)}^2}}$
• C. $r=\frac{N\sum \left(X_i{Y}_i\right)–(\sum X_i)(\sum Y_i)}{(N\sum X_i^2–(\sum X_i{)}^2\left)\right(N\sum Y_i^2–(\sum Y_i{)}^2)}$
• D. $r=\frac{N\sum \left(X_i{Y}_i\right)–N(\sum X_i)(\sum Y_i)}{(N\sum X_i^2–(\sum X_i{)}^2\left)\right(N\sum Y_i^2–(\sum Y_i{)}^2)}$

Answer 1

The correct option is A

$r=\frac{N\sum \left(X_i{Y}_i\right)–(\sum X_i)(\sum Y_i)}{\sqrt{N\sum X_i^2–(\sum X_i{)}^2}\sqrt{N\sum Y_i^2–(\sum Y_i{)}^2}}$

$r=\frac{N\sum \left(X_i{Y}_i\right)–(\sum X_i)(\sum Y_i)}{\sqrt{N\sum X_i^2–(\sum X_i{)}^2}\sqrt{N\sum Y_i^2–(\sum Y_i{)}^2}}$
This is the Karl Pearson's formula for calculating r.