Polynomial Regression

Polynomial Regression is a form of regression where the relationship between the dependent variable y and the independent variable x is modeled as an nth degree polynomial.

Formula for Polynomial Regression



Code snippet

from sklearn.preprocessing import PolynomialFeatures
poly_regr = PolynomialFeatures(degree = 2)
X_poly = poly_regr.fit_transform(X)
poly_regr.fit(X_poly, y)
reg = LinearRegression()

reg.fit(X_poly, y)

degree is the degree of the polynomial features.

Refer plots below with varying degree and observe that as degree value increases, the curve becomes more aligned to the data

Degree 2

Degree 3

Degree 4

Degree 5

Multiple Linear Regression

Multiple Linear Regression is a regression model where we have multiple independent variables.

We need to predict values for the dependent variable as a function of the independent variables.



Formula for Multiple Linear Regression:

where

y is the dependent Variable

 onwards are the the independent Variable

 onwards is the coefficient (connector between dependent and Independent)

 is the Constant

Always encode the categorical data if any after data import.

Code Snippet:

from sklearn.linear_model import LinearRegression

multi_regressor = LinearRegression()

multi_regressor.fit(X_train, y_train)

# Prediction

y_pred = multi_regressor.predict(X_test)

Simple Linear Regression

Simple Linear Regression is a linear regression model where we have one dependent and one independent variable.

We need to predict values for the dependent variable as a function of the independent variable.



Formula for Simple Linear Regression:

where

y is the dependent Variable

 is the independent Variable

 is the coefficient (connector between dependent and Independent)

 is the Constant

Code Snippet:

from sklearn.linear_model import LinearRegression

simple_regressor = LinearRegression()

simple_regressor.fit(X_train, y_train)

# Prediction

y_pred = simple_regressor.predict(X_test)

Plot

plt.scatter(X_test, y_test, color = 'red')

plt.plot(X_train, simple_regressor.predict(X_train), color = 'blue')

plt.show()