Multi-Linear Regression

Multiple Variables Linear Regression
Author

Benedict Thekkel

Sample problem of predicting home price in monroe, new jersey (USA)

Below is the table containing home prices in monroe twp, NJ. Here price depends on area (square feet), bed rooms and age of the home (in years). Given these prices we have to predict prices of new homes based on area, bed rooms and age.

Given these home prices find out price of a home that has,

3000 sqr ft area, 3 bedrooms, 40 year old

2500 sqr ft area, 4 bedrooms, 5 year old

We will use regression with multiple variables here. Price can be calculated using following equation,

Here area, bedrooms, age are called independant variables or features whereas price is a dependant variable

import pandas as pd
import numpy as np
from sklearn import linear_model
df = pd.read_csv('./Data/homeprices.csv')
df
area bedrooms age price
0 2600 3.0 20 550000
1 3000 4.0 15 565000
2 3200 NaN 18 610000
3 3600 3.0 30 595000
4 4000 5.0 8 760000
5 4100 6.0 8 810000

Data Preprocessing: Fill NA values with median value of a column

df.bedrooms.median()
4.0
df.bedrooms = df.bedrooms.fillna(df.bedrooms.median())
df
area bedrooms age price
0 2600 3.0 20 550000
1 3000 4.0 15 565000
2 3200 4.0 18 610000
3 3600 3.0 30 595000
4 4000 5.0 8 760000
5 4100 6.0 8 810000 
reg = linear_model.LinearRegression()
reg.fit(df.drop('price',axis='columns'),df.price)
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
reg.coef_
array([  112.06244194, 23388.88007794, -3231.71790863])
reg.intercept_
221323.00186540408

Find price of home with 3000 sqr ft area, 3 bedrooms, 40 year old

reg.predict([[3000, 3, 40]])
/home/ben/mambaforge/envs/cfast/lib/python3.11/site-packages/sklearn/base.py:464: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(
array([498408.25158031])
112.06244194*3000 + 23388.88007794*3 + -3231.71790863*40 + 221323.00186540384
498408.25157402386

Find price of home with 2500 sqr ft area, 4 bedrooms, 5 year old

reg.predict([[2500, 4, 5]])
/home/ben/mambaforge/envs/cfast/lib/python3.11/site-packages/sklearn/base.py:464: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(
array([578876.03748933])
np.set_printoptions(precision=2, suppress=True)
corrcoef = np.corrcoef(df, rowvar=False)
corrcoef
array([[ 1.  ,  0.75, -0.45,  0.9 ],
       [ 0.75,  1.  , -0.88,  0.92],
       [-0.45, -0.88,  1.  , -0.73],
       [ 0.9 ,  0.92, -0.73,  1.  ]])
import matplotlib.pyplot as plt
import seaborn as sn
df.columns
Index(['area', 'bedrooms', 'age', 'price'], dtype='object')
plt.figure(figsize=(7,5))
sn.heatmap(corrcoef, annot=True)

plt.xticks(range(len(df.columns)), df.columns)
plt.yticks(range(len(df.columns)), df.columns)
# Move x-axis ticks and labels to the top
plt.gca().xaxis.set_ticks_position('top')


plt.show()

Exercise

In exercise folder (same level as this notebook on github) there is hiring.csv. This file contains hiring statics for a firm such as experience of candidate, his written test score and personal interview score. Based on these 3 factors, HR will decide the salary. Given this data, you need to build a machine learning model for HR department that can help them decide salaries for future candidates. Using this predict salaries for following candidates,

2 yr experience, 9 test score, 6 interview score

12 yr experience, 10 test score, 10 interview score

Answer

53713.86 and 93747.79

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