In supervised learning, you start with fixed inputs and outputs. By running your data through a learning algorithm, you create a hypothesis—a model's "brain" that makes its own inputs and outputs based on the training data.
What is a Hypothesis?
A hypothesis in linear regression is shown as:
h(x) = θ0 + θ1x1
Here’s what the symbols mean:
h is the hypothesis, the model's memory formed after training.
x is the input given to the hypothesis.
θ (theta) are the important parameters for the model.
This formula works well when your input has one parameter.
Extending to Multiple Attributes
When working with datasets with multiple attributes, the hypothesis extends to:
h(x) = ∑(j=0 to m)θj*xj
Where:
m is the number of attributes (features) in your dataset.
θj are the parameters for each attribute xj.
In this extended formula:
θ0 is the intercept term (bias).
θ1, θ2, …, θm are the weights for each attribute.
To sum up, the hypothesis in linear regression can be shown simply as h(x) = θ0 + θ1x for a single input parameter. For datasets with multiple attributes, it generalizes to: h(x) = ∑(j=0 to m)θj*xj
Understanding these representations is key for building and improving machine learning models using linear regression.