Python for Data Science

Chapter 3 - Regressoin Models

Segment 1 - Simple linear regression

Linear Regression

Linear regression is a statistical machine learning method you can use to quantify, and make predictions based on, relationships between numerical variables.

Simple linear regression
Multiple linear regression

Linear Regression Use Cases

Sales Forecasting
Supply Cost Forecasting
Resource Consumption Forecasting
Telecom Services Lifecycle Forecasting

Linear Regression Assumptions

All variables are continuous numeric, not categorical
Data is free of missing values and outliers
There's a linear relationship between predictors and predictant
All predictors are independent of each other
Residuals(or prediction errors) are normally distributed

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import sklearn

from pylab import rcParams
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import scale

%matplotlib inline
rcParams['figure.figsize'] = 10,8

rooms = 2*np.random.rand(100,1)+3
rooms[1:10]

array([[3.24615481],
       [4.86219627],
       [3.17742366],
       [3.03114054],
       [3.73270016],
       [3.58047146],
       [3.23240264],
       [4.63462537],
       [3.91227449]])

price = 265 + 6*rooms + abs(np.random.randn(100,1))
price[1:10]

array([[285.23677074],
       [294.79616144],
       [284.85274605],
       [284.40046371],
       [288.07421652],
       [286.60487136],
       [284.55567969],
       [293.27121913],
       [289.12143579]])

plt.plot(rooms,price,'r^')
plt.xlabel("# of Rooms, 2019 Average")
plt.ylabel("2019 Average Home, 1000s USD")
plt.show()

ML0301output_5_0

X = rooms
y = price

LinReg = LinearRegression()
LinReg.fit(X,y)
print(LinReg.intercept_, LinReg.coef_)

[266.13626468] [[5.9306674]]

Simple Algebra

y = mx + b
b = intercept = 266.7

Estimated Coefficients

LinReg.coef_ = [5.93] Estimated coefficients for the terms in the linear regression problem.

print(LinReg.score(X,y))

0.961246701242803