{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Päivitetty 2024-04-02 / Aki Taanila\n"
]
}
],
"source": [
"from datetime import datetime\n",
"print(f'Päivitetty {datetime.now().date()} / Aki Taanila')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lineaarinen regressio - yksi selittävä muuttuja\n",
"\n",
"Lineaarisessa regressiossa sovitetaan suora viiva kuvaamaan selittävän muuttujan ja ennustettavan muuttujan välistä yhteyttä. Yleensä käytetään suoran sovitukseen pienimmän neliösumman menetelmää, joka minimoi ennustevirheiden neliöiden summan."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set_style('whitegrid')\n",
"\n",
"# Tuon lineaarisen regressiomallin\n",
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Datan tarkastelua\n",
"\n",
"Tavoitteena ennustaa myynti mainoskulujen perusteella."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Kuukausi | \n",
" Mainoskulut 1000 € | \n",
" Myynti 1000 € | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 1 | \n",
" 1.2 | \n",
" 101 | \n",
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" | 1 | \n",
" 2 | \n",
" 0.8 | \n",
" 92 | \n",
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\n",
" \n",
" | 2 | \n",
" 3 | \n",
" 1.0 | \n",
" 110 | \n",
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\n",
" \n",
" | 3 | \n",
" 4 | \n",
" 1.3 | \n",
" 120 | \n",
"
\n",
" \n",
" | 4 | \n",
" 5 | \n",
" 0.7 | \n",
" 90 | \n",
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" \n",
" | 5 | \n",
" 6 | \n",
" 0.8 | \n",
" 82 | \n",
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" \n",
" | 6 | \n",
" 7 | \n",
" 1.0 | \n",
" 93 | \n",
"
\n",
" \n",
" | 7 | \n",
" 8 | \n",
" 0.6 | \n",
" 75 | \n",
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\n",
" \n",
" | 8 | \n",
" 9 | \n",
" 0.9 | \n",
" 91 | \n",
"
\n",
" \n",
" | 9 | \n",
" 10 | \n",
" 1.1 | \n",
" 105 | \n",
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\n",
" \n",
"
\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Riippuvuuden tarkastelua seaborn-kirjaston jointoplot-kaavion avulla\n",
"sns.jointplot(data=df, x='Mainoskulut 1000 €', y='Myynti 1000 €', kind='reg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mallin sovitus"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Selittävä muuttuja\n",
"# Jos selittäviä muuttujia on vain yksi, niin tarvitaan dataframeksi muuntaminen (to_frame)\n",
"X = df['Mainoskulut 1000 €'].to_frame()\n",
"\n",
"# Ennustettava muuttuja\n",
"y = df['Myynti 1000 €'] "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"malli = LinearRegression().fit(X,y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mallin tarkastelua"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([52.56756757])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"malli.coef_ # regressiosuoran kulmakerroin"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Mallin mukaan yhden yksikön (1000 €) kasvu mainoskuluissa lisää myyntiä noin 52,6 yksiköllä (1000 €)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"46.486486486486505"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"malli.intercept_ # regressiosuoran vakiotermi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Jos mainoskuluja ei ole lainkaan, niin mallin mukainen myynti on noin 46,5 yksikköä (1000 €). Tähän tietoon täytyy suhtautua varoen, koska havainnoissa ei ole mukana nollan lähellä olevia mainoskuluja. Näin ollen ei voida tietää päteekö suoraviivainen riippuvuus mainoskulujen 0 lähellä."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7663982928521625"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"malli.score(X,y) # selityskerroin"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Myynnin vaihtelusta noin 76,6 % voidaan selittää mainoskulujen vaihtelulla."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mallin käyttö ennustamiseen"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
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\n",
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Lisätietoa
\n",
"\n",
"Data-analytiikka Pythonilla: https://tilastoapu.wordpress.com/python/"
]
}
],
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