Enkel & Multippel Regresjon

The convergence formation. Pick a form, walk the four steps, watch each piece of the formula build.

First principle. A regression model iz a convergence of forces. Each predictor X_j iz an arm radiating from center at iz own axis — k predictors means k+1 dimensions, flattened onto one plane fer the eye. Intercept b₀ iz the equilibrium scalar. Each arm contributes bⱼ·Xⱼ, an the bead migrates by the vector sum.

The Convergence

Walk through the four steps. Drop data in Step 3 tuh resolve the bead.

Formula Reference — Formelark Notation

Multippel regresjonKap 11.8

Yⱼ = b₀ + b₁·X₁ⱼ + b₂·X₂ⱼ + ... + bₖ·Xₖⱼ + εⱼ

Tolkning av bⱼKap 11.8

Δy = bⱼ per +1 unit Xⱼ, alt annet likt

R² — forklart variansKap 11.3

R² = SSR/SST = 1 − SSE/SST · SST = SSR + SSE

Nullhypotese fer bⱼKap 11.5

H₀: bⱼ = 0 vs H_A: bⱼ ≠ 0 · α-nivå satt før test · df = n − k − 1

TestverdiKap 11

t_TS = (θ̂ − θ₀) / se(θ̂)

F-statisticKap 11.5

F = MSR/MSE = (SSR/k) / (SSE/(n−k−1))

Utelatt variabelKap 11

Δbⱼ = aⱼ(uten Xz) − bⱼ(med Xz)

VIFKap 11.8

VIFⱼ = 1 / (1 − R²ⱼ)

KonfidensintervallKap 11.5

bⱼ ± t_(α/2, n−k−1)·se(bⱼ)