Berilganlarni intellektual tahlili fanidan Ko’p chiziqli regressiya

Model qanchalik muhim?
F -nisbati regressiya modelining statistik ahamiyatini baholaydi va ANOVA jadvalidagi o'rtacha kvadratik shartlardan hisoblanadi. F-nisbatining ahamiyati ikki darajadagi erkinlik ( df MSR , df MSE )yordamida F taqsimot jadvaliga murojaat qilish orqali olinadi. p - mustaqil o'zgaruvchilar soni (masalan, p oddiy chiziqli regressiya uchun bitta).

F-nisbatining dan ustunligi shundaki, F-nisbati regressiya modelining ahamiyatini baholashda tanlanma hajmi va bashorat qiluvchilar sonini o'z ichiga oladi. Model yuqori R ^2 ga ega bo'lishi mumkin va hali ham statistik ahamiyatga ega emas.
Koeffitsientlar qanchalik muhim?
Agar regressiya modeli sezilarli darajada yaxshi bo'lsa, biz har bir koeffitsientning statistik ahamiyatini baholash uchun t-testidan foydalanishimiz mumkin.
Ko'p chiziqlilik
Bashorat qiluvchilar o'rtasidagi yuqori darajadagi multikolinearlik ishonchsiz regressiya koeffitsientini baholaydi. Multikolinearlik belgilariga quyidagilar kiradi:
1. Bashorat qiluvchi o'zgaruvchilar juftlari o'rtasidagi yuqori korrelyatsiya. 2. Belgilari yoki kattaliklari yaxshi jismoniy ma'noga ega bo'lmagan R egressiya koeffitsientlari. 3. Muhim bashorat qiluvchilar bo'yicha statistik jihatdan ahamiyatsiz regressiya koeffitsientlari. 4. Regressiya koeffitsientlarining belgisi yoki kattaligining bashoratchini kiritish yoki o'chirishga o'ta sezgirligi.
matritsadagi diagonal qiymatlar Variant inflyatsiya omillari (VIFs) deb ataladi  va ular ko'p chiziqlilikning juda foydali o'lchovidir. Agar har qanday VIF 5 dan oshsa, multikolinearlik muammo hisoblanadi.
Model tanlash
Ma'lumotlarni qazib olishda tez-tez uchraydigan muammo bu modelni bashorat qilishga sezilarli hissa qo'shmaydigan bashorat qiluvchilardan qochishdir. Birinchidan, arzimas koeffitsientlarga ega bo'lgan bashoratchilarni tushirish bashoratlarning o'rtacha xatosini kamaytirishi mumkinligi ko'rsatilgan. Ikkinchidan, ko'p o'zgaruvchilarga ega modellarda ko'p kollinearlik tufayli regressiya koeffitsientlarini baholash beqaror bo'lishi mumkin.  Va nihoyat, oddiyroq model - bu modellardagi bashorat qiluvchilarning ta'sirini ko'proq tushunadigan yaxshi model. Modelni tanlashning ikkita asosiy usuli mavjud:
Oldinga tanlash, eng yaxshi bashorat qiluvchilar modelga birma-bir kiritiladi. Orqaga barham berish, eng yomon bashorat qiluvchilar modeldan birma-bir chiqarib tashlanadi.

Misol:{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"import statistics\n",
"import pandas as pd\n",
"from matplotlib import pyplot as plt\n",
"import seaborn as sns\n",
"import numpy as np\n",
"from scipy import stats\n",
"from sklearn.linear_model import LinearRegression\n",
"from sklearn import metrics\n",
"import scikitplot as skplt\n",
"from sklearn import tree\n",
"from sklearn.datasets import make_regression\n",
"from sklearn.metrics import mean_squared_error\n",
"import statsmodels.api as sm"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Download the data from http://www.saedsayad.com/datasets/BikeRental.zip\n",
"trainset=pd.read_csv('C:\\\\Users\\\\Lenovo\\\\Documents\\\\Python Codes\\\\BikeRental\\\\bike_rental_train.csv')\n",
"testset=pd.read_csv('C:\\\\Users\\\\Lenovo\\\\Documents\\\\Python Codes\\\\BikeRental\\\\bike_rental_test.csv')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"trainset.shape\n",
"testset.shape"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"trainset.columns\n",
"testset.columns"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# training\n",
"cols=['temp', 'humidity', 'windspeed']\n",
"tr=trainset.dropna(axis=0,how='any')\n",
"X_train=tr[cols]\n",
"y_train=tr['bike_rent_count']"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"mlr = LinearRegression()\n",
"mlr.fit(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# show the model parameters\n",
"print(mlr.intercept_, mlr.coef_, mlr.score(X_train, y_train))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# testing\n",
"cols=['temp', 'humidity', 'windspeed']\n",
"ts=testset.dropna(axis=0,how='any')\n",
"X_test=ts[cols]\n",
"y_test=ts['bike_rent_count']\n",
"y_pred = mlr.predict(X_test)\n",
"print('R-squared of multiple linear regression on test set: {:.2f}'.format(mlr.score(X_test, y_test)))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# mean squared error\n",
"mse = mean_squared_error(y_test, y_pred)\n",
"print(\"MSE: \", mse)\n",
"print(\"RMSE: \", mse**(1/2.0)) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot original and predicted values\n",
"x_ax = range(len(y_test))\n",
"plt.plot(x_ax, y_test, label=\"original\")\n",
"plt.plot(x_ax, y_pred, label=\"predicted\")\n",
"plt.title(\"test and predicted data\")\n",
"plt.xlabel('X-axis')\n",
"plt.ylabel('Y-axis')\n",
"plt.legend(loc='best',fancybox=True, shadow=True)\n",
"plt.grid(True)\n",
"plt.show() "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# residulas\n",
"res=y_test-y_pred\n",
"sns.histplot(res)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sns.boxplot(x=res, showmeans=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"mu, std = stats.norm.fit(res)\n",
"fig, ax = plt.subplots()\n",
"\n",
"# plot the residuals\n",
"sns.histplot(x=res, ax=ax, stat=\"density\", linewidth=0, kde=True)\n",
"ax.set(title=\"Distribution of residuals\", xlabel=\"residual\")\n",
"\n",
"# plot corresponding normal curve\n",
"xmin, xmax = plt.xlim() # the maximum x values from the histogram above\n",
"x = np.linspace(xmin, xmax, 100) # generate some x values\n",
"p = stats.norm.pdf(x, mu, std) # calculate the y values for the normal curve\n",
"sns.lineplot(x=x, y=p, color=\"orange\", ax=ax)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Q-Q plot\n",
"sm.qqplot(res, line='s')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# scatter plot\n",
"plt.scatter(y_test,y_pred)"
]
}
],
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"kernelspec": {
"display_name": "Python 3.11.0 64-bit",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.0"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "e956c49ae0caa224b5fdd754cbc353d7e61c6c61f7329ee680c7f7b4f1b71a8e" }
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