Linear Correlation
Gujarat Board · Class 12 · Statistics
All formulas from Linear Correlation in Gujarat Board Class 12 Statistics. Key equations, constants, and identities for board exam preparation.
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Formulas
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)]
R = 1 - [6(ΣD² + CF)] / [n(n²-1)]
CF = Σ (m³ - m)/12
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