Introduction to Simple Linear Regression
Basically, the formula for a straight line with:
- : Dependent Variable (DV)
- : Constant
- : Coefficient of IV. Represents how a unit change in effects a unit change in .
- : Independent Variable (IV)
Simple Linear Regression is a method of finding a line that best fits a set of data points on the graph. The methodology in getting the line of best fit is simple. Let’s say we drew a vertical line from all our points to our guess line. The distance can be written where i represents the point number. For the line to be the line of best fit is if the value of the following formula is the lowest it can possibly be:
( - –> min
Called the Orderly Least Square Method
Creating a simple Linear Regression in Python
First we need to preprocess the data using the preprocessing template:
#Importing the libraries import numpy as np import matplotlib.pyplot as plt import pandas as pd #Importing the dataset dataset = pd.read_csv('Data.csv') X = dataset.iloc[:, :-1].values y = dataset.iloc[:, 3].values #Taking care of missing data from sklearn.preprocessing import Imputer imputer = Imputer(missing_values = 'NaN', strategy = 'mean', axis = 0) imputer = imputer.fit(X[:, 1:3]) X[:, 1:3] = imputer.transform(X[:, 1:3]) #Encoding categorical data #Encoding the Independent Variable from sklearn.preprocessing import LabelEncoder, OneHotEncoder labelencoder_X = LabelEncoder() X[:, 0] = labelencoder_X.fit_transform(X[:, 0]) onehotencoder = OneHotEncoder(categorical_features = ) X = onehotencoder.fit_transform(X).toarray() #Encoding the Dependent Variable labelencoder_y = LabelEncoder() y = labelencoder_y.fit_transform(y) #Splitting the dataset into the Training set and Test set from sklearn.cross_validation import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0) #Feature Scaling from sklearn.preprocessing import StandardScaler sc_X = StandardScaler() X_train = sc_X.fit_transform(X_train) X_test = sc_X.transform(X_test) sc_y = StandardScaler() y_train = sc_y.fit_transform(y_train)
Note: We do not to perform feature scaling, the scikit learn library will handle that for us.
LinearRegression library from SciKit-Learn.
from sklearn.linear_model import LinearRegression
Create object of class and fit it to the training set
regressor = LinearRegression() regressor = regressor.fit(X_train, y_train)
Now we need to create a vector that contains the predictions of the test set. (Contains predicted values of test set. With the matrix of text set X.
y_pred = regressor.predict(X_test)
y_pred will be out predicted results and
y_test will be our actual results.