Linear Correlation — Formula Sheet
Gujarat Board · Class 12 · Statistics
9 formulas from Linear Correlation (Gujarat Board Class 12 Statistics) on one page, grouped by topic. Includes Property 1 (Range) and Property 3.
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Formulas and Key Relations
Karl Pearson's Product Moment Method
r = Cov(X,Y) / (σx × σy)
r = Σ(xi - x̄)(yi - ȳ) / √[Σ(xi - x̄)² × Σ(yi - ȳ)²]
r = [nΣxiyi - (Σxi)(Σyi)] / √{[nΣxi² - (Σxi)²][nΣyi² - (Σyi)²]}
r = Σuivi / √(Σui² × Σvi²) where ui = xi - A, vi = yi - B
r = [nΣuivi - (Σui)(Σvi)] / √{[nΣui² - (Σui)²][nΣvi² - (Σvi)²]}
Spearman's Rank Correlation Method
R = 1 - [6ΣD²] / [n(n²-1)]
CF = Σ (m³ - m)/12
Properties of Correlation Coefficient – Detailed Study
Property 1 (Range)
-1 ≤ r ≤ 1. This is the most fundamental property.
Property 3 (Symmetry)
r(X,Y) = r(Y,X). It does not matter which variable is X and which is Y.
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