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.
Note
Consider n to be a whole number greater than two.
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.
However, we live in a 3-dimensional world and cannot imagine higher-dimensional plots.
Anyway, it is unnecessary 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 helps us with it.
Normal Equation
Compared to the Normal Equation we used for Simple Linear Regression, only the X̃ matrix has changed.
Again, we will not dive into the maths behind it; the point is, finding parameters for n-feature Linear Regression uses the same approach as for Simple Linear Regression (but is a little more computationally expensive).
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Completion rate improved to 5.56Linear Regression with n Features
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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.
Note
Consider n to be a whole number greater than two.
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.
However, we live in a 3-dimensional world and cannot imagine higher-dimensional plots.
Anyway, it is unnecessary 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 helps us with it.
Normal Equation
Compared to the Normal Equation we used for Simple Linear Regression, only the X̃ matrix has changed.
Again, we will not dive into the maths behind it; the point is, finding parameters for n-feature Linear Regression uses the same approach as for Simple Linear Regression (but is a little more computationally expensive).
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