Linear Regression
Gujarat Board · Class 12 · Statistics
All formulas from Linear Regression in Gujarat Board Class 12 Statistics. Key equations, constants, and identities for board exam preparation.
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Formulas
Regression Line & Regression Coefficient Formulae
Ŷ = a + bX
b = [n·ΣXY − ΣX·ΣY] / [n·ΣX² − (ΣX)²]
a = Ȳ − b·X̄
b = Cov(X,Y) / Var(X) = σxy / σx²
b = r · (σy / σx)
Short-Cut Method (Change of Origin and Scale)
If U = X − A and V = Y − B, then b = [n·ΣUV − ΣU·ΣV] / [n·ΣU² − (ΣU)²]
If U = (X − A)/C and V = (Y − B)/D, then b = (D/C) · [n·ΣUV − ΣU·ΣV] / [n·ΣU² − (ΣU)²]
Coefficient of Determination
r² = (Coefficient of Determination)
% variation explained = r² × 100
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