Machine Learning || Multiple Linear Regression Model

How to Create a Multi-Polynomial Regression Model

Introduction to Multi-Polynomial Regression

• The video aims to teach viewers how to create a multi-polynomial regression model that is faster and stronger than the simple regression model discussed in previous videos.

• Viewers are encouraged to prepare their materials, including tea and notebooks, for the session.

Recap of Simple Linear Regression

• The presenter welcomes viewers and recaps that previous models used only one input feature, such as house size, to predict house prices.

• In contrast, today's example will utilize multiple input features rather than just one.

Understanding Input Features

• Multiple input features can enhance predictions; examples include the number of floors and the age of the house.

• Each case (or observation) can have several input features represented as x_1, x_2, ldots .

Notation for Input Features

• The notation x^(j) indicates an input feature for a specific case. For instance, if j = 1 , it refers to all values in the first column across cases.

• If there are four input features in total, they can be denoted as n_small = 4 .

Transitioning from Simple to Multi Polynomial Regression

• In simple linear regression, the equation was expressed as f(w|x)=w*x + b . However, with multiple features:

• The equation becomes:

• f(w|x)=b + w_1x_1 + w_2x_2 + w_3x_3 + w_4x_4 .

Example of a Multi Polynomial Regression Model

• An example model might look like:

• f(w|x)=1/10x_1 + 4x_2 + 10x_3 - 2x_4 + 80 .

Interpreting Coefficients and Predictions

• Each coefficient represents how much each feature contributes to predicting house prices. For instance:

• A base price (when all inputs are zero): $80,000.

Impact of Input Features on House Price Prediction

• Changes in any feature will adjust the predicted price. For example:

• Increasing size by one unit raises the price by $1000 multiplied by its coefficient.

Conclusion on Feature Influence

• As more bedrooms or floors increase in number:

Understanding House Pricing and Regression Models

The Relationship Between House Age and Price

• The price of a house decreases as its age increases, represented by the equation where the price is reduced by $2000 for each unit increase in age.

• A polynomial function is used to model this relationship, indicating that older houses tend to have lower prices.

Simplifying Complex Equations

• The discussion introduces multiple emotions (variables), leading to a modern weighted equation: W(X) = W_1X_1 + 2X_2 + ... + W_nX_n .

• It explains the concept of a vector containing all weights W , from W_1 to W_n , while another parameter, B , represents a single number.

Vector Representation in Models

• A second vector, denoted as X , contains values from X_1 to X_n . This allows for structured representation of data points.

• The multiplication of corresponding elements in vectors leads to simplified models, specifically highlighting the multi-polynomial regression model distinct from multiple linear regression.

Conclusion and Engagement

• The speaker encourages viewers to leave comments for questions and feedback on the video content.