Chiziqli regressiya

bashorat = w1 · maydon + w2 · xonalar + ... + b

MSE = (1/n) · Σ (haqiqiy - bashorat)²

import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, r2_score

np.random.seed(42)

# Ma'lumot
n = 200
maydon = np.random.uniform(40, 150, n)
narx = maydon * 8.5 + np.random.normal(0, 70, n) + 120

X = maydon.reshape(-1, 1)
y = narx

X_oqitish, X_sinov, y_oqitish, y_sinov = train_test_split(
    X, y, test_size=0.2, random_state=42
)

# O'qitish
model = LinearRegression()
model.fit(X_oqitish, y_oqitish)

print(f"Koeffitsiyent (w): {model.coef_[0]:.2f}")
print(f"Kesishma (b):      {model.intercept_:.2f}")

bashorat = model.predict(X_sinov)

print(f"MSE:  {mean_squared_error(y_sinov, bashorat):.1f}")
print(f"RMSE: {np.sqrt(mean_squared_error(y_sinov, bashorat)):.1f}")
print(f"R2:   {r2_score(y_sinov, bashorat):.3f}")

from sklearn.metrics import mean_absolute_error

print(f"MAE:  {mean_absolute_error(y_sinov, bashorat):.1f}")
print(f"RMSE: {np.sqrt(mean_squared_error(y_sinov, bashorat)):.1f}")

def gradient_tushish(X, y, tezlik=0.0001, qadamlar=1000):
    n = len(X)
    w = 0.0
    b = 0.0

    for qadam in range(qadamlar):
        bashorat = w * X + b
        xato = bashorat - y

        # Hosilalar
        dw = (2 / n) * np.sum(xato * X)
        db = (2 / n) * np.sum(xato)

        # Yangilash
        w -= tezlik * dw
        b -= tezlik * db

        if qadam % 200 == 0:
            mse = np.mean(xato ** 2)
            print(f"Qadam {qadam:4d}: w={w:6.2f}  b={b:6.2f}  MSE={mse:9.1f}")

    return w, b


w, b = gradient_tushish(maydon, narx)

qoldiqlar = y_sinov - bashorat

import matplotlib.pyplot as plt

fig, oyna = plt.subplots(1, 2, figsize=(12, 4))

oyna[0].scatter(bashorat, qoldiqlar, alpha=0.6)
oyna[0].axhline(0, color="red", linestyle="--")
oyna[0].set_xlabel("Bashorat")
oyna[0].set_ylabel("Qoldiq")
oyna[0].set_title("Qoldiqlar taqsimoti")

oyna[1].hist(qoldiqlar, bins=25, color="steelblue", edgecolor="white")
oyna[1].set_title("Qoldiqlar gistogrammasi")

plt.tight_layout()
plt.show()

uylar = pd.DataFrame({
    "maydon":  np.random.uniform(40, 150, 300),
    "xonalar": np.random.randint(1, 5, 300),
    "yosh":    np.random.randint(0, 40, 300),
})
uylar["narx"] = (
    uylar["maydon"] * 8
    + uylar["xonalar"] * 25
    - uylar["yosh"] * 4
    + np.random.normal(0, 40, 300)
    + 100
)

X = uylar[["maydon", "xonalar", "yosh"]]
y = uylar["narx"]

model = LinearRegression()
model.fit(X, y)

for belgi, vazn in zip(X.columns, model.coef_):
    print(f"{belgi:10s}: {vazn:7.2f}")
print(f"{'kesishma':10s}: {model.intercept_:7.2f}")

# Bitta belgi
model_1 = LinearRegression().fit(uylar[["maydon"]], y)
print(f"Faqat maydon:  R2 = {model_1.score(uylar[['maydon']], y):.3f}")

# Uchta belgi
model_3 = LinearRegression().fit(X, y)
print(f"Uchta belgi:   R2 = {model_3.score(X, y):.3f}")

# Multikollinearlikni tekshirish
print(X.corr().round(2))

from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler

X_oqitish, X_sinov, y_oqitish, y_sinov = train_test_split(
    X, y, test_size=0.2, random_state=42
)

quvur = Pipeline([
    ("masshtab", StandardScaler()),
    ("model", LinearRegression()),
])

quvur.fit(X_oqitish, y_oqitish)

bashorat_oqitish = quvur.predict(X_oqitish)
bashorat_sinov   = quvur.predict(X_sinov)

print(f"O'qitish R2: {r2_score(y_oqitish, bashorat_oqitish):.3f}")
print(f"Sinov R2:    {r2_score(y_sinov, bashorat_sinov):.3f}")
print(f"Sinov RMSE:  {np.sqrt(mean_squared_error(y_sinov, bashorat_sinov)):.1f}")