Regresion Lineal Multiple Ejercicios Resueltos A Mano 🌟

Para dos predictores, podemos resolver el sistema de ecuaciones normales:

Datos nuevos (y realistas):
Y = Precio de vivienda (miles $), X₁ = metros cuadrados, X₂ = antigüedad (años).

| i | Y | X₁ | X₂ | |---|----|----|----| | 1 | 120| 80 | 10 | | 2 | 150| 100| 5 | | 3 | 90 | 60 | 15 | | 4 | 200| 140| 2 | | 5 | 110| 85 | 8 | regresion lineal multiple ejercicios resueltos a mano

| ( X_1 ) | ( X_2 ) | ( Y ) | ( X_1Y ) | ( X_2Y ) | ( X_1X_2 ) | ( X_1^2 ) | ( X_2^2 ) | |----------|----------|--------|-----------|-----------|-------------|------------|------------| | 2 | 6 | 65 | 130 | 390 | 12 | 4 | 36 | | 3 | 7 | 70 | 210 | 490 | 21 | 9 | 49 | | 4 | 7 | 75 | 300 | 525 | 28 | 16 | 49 | | 5 | 8 | 80 | 400 | 640 | 40 | 25 | 64 | | 6 | 8 | 85 | 510 | 680 | 48 | 36 | 64 | | Σ=20 | Σ=36 | Σ=375 | Σ=1550 | Σ=2725 | Σ=149 | Σ=90 | Σ=262 |

( n = 5 )

| Student | (X_1) | (X_2) | (Y) | (X_1Y) | (X_2Y) | (X_1^2) | (X_2^2) | (X_1X_2) | |---------|---------|---------|-------|----------|----------|----------|----------|------------| | 1 | 4 | 6 | 75 | 300 | 450 | 16 | 36 | 24 | | 2 | 6 | 5 | 85 | 510 | 425 | 36 | 25 | 30 | | 3 | 2 | 8 | 65 | 130 | 520 | 4 | 64 | 16 | | 4 | 5 | 7 | 80 | 400 | 560 | 25 | 49 | 35 | | 5 | 3 | 6 | 70 | 210 | 420 | 9 | 36 | 18 | | Sum | 20 | 32 | 375 | 1550 | 2375 | 90 | 210 | 123 |

So:

The design matrix $X$ includes a column of 1s (intercept), then $X_1$ and $X_2$:

$$ X = \beginbmatrix 1 & 2 & 1 \ 1 & 3 & 2 \ 1 & 5 & 3 \ 1 & 7 & 4 \ 1 & 8 & 5 \endbmatrix $$ Para dos predictores, podemos resolver el sistema de

$$ Y = \beginbmatrix 70 \ 75 \ 85 \ 95 \ 100 \endbmatrix $$