Linear Regression with N Features
N-Feature Linear Regression Equation
As we have seen, adding the new feature to the linear regression model is as easy as adding it along with the new parameter to the model's equation. We can add much more than two parameters that way.
Consider n to be a whole number greater than two.
Normal Equation
The only problem is the visualization. If we have two parameters, we need to build a 3D plot. But if we have more than two parameters, the plot will be more than three-dimensional. But we live in a 3-dimensional world and cannot imagine higher-dimensional plots. However, it is not necessary to visualize the result. We only need to find the parameters for the model to work. Luckily, it is relatively easy to find them. The good old Normal Equation will help us:
X̃ Matrix
Notice that only the X̃ matrix has changed. You can think of the columns of this matrix as each responsible for its β parameter. The following video explains what I mean.
The first column of 1s is needed to find the β₀ parameter.
Danke für Ihr Feedback!
Fragen Sie AI
Fragen Sie AI
Fragen Sie alles oder probieren Sie eine der vorgeschlagenen Fragen, um unser Gespräch zu beginnen
Großartig!
Completion Rate verbessert auf 6.67Linear Regression with N Features
Swipe um das Menü anzuzeigen
N-Feature Linear Regression Equation
As we have seen, adding the new feature to the linear regression model is as easy as adding it along with the new parameter to the model's equation. We can add much more than two parameters that way.
Consider n to be a whole number greater than two.
Normal Equation
The only problem is the visualization. If we have two parameters, we need to build a 3D plot. But if we have more than two parameters, the plot will be more than three-dimensional. But we live in a 3-dimensional world and cannot imagine higher-dimensional plots. However, it is not necessary to visualize the result. We only need to find the parameters for the model to work. Luckily, it is relatively easy to find them. The good old Normal Equation will help us:
X̃ Matrix
Notice that only the X̃ matrix has changed. You can think of the columns of this matrix as each responsible for its β parameter. The following video explains what I mean.
The first column of 1s is needed to find the β₀ parameter.
Danke für Ihr Feedback!
