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The connection between the linear part and the activation part in a neural network involves the process of transforming the weighted sum of input features (the linear part) into an output that is suitable for the task at hand, often by introducing non-linearity.

	Inputs of neural network (linear, z)		Output of neural network (activation function, a)
		a = σ(z)
	z = b + w1​x1​​ + w2​​x2​​ + … + wn​xn​
	The linear part provides the model with the capacity to capture linear relationships between the input features and the output.		The activation part, by applying a non-linear function like the sigmoid, introduces complexity and flexibility into the model. This is important because many real-world relationships are not strictly linear.

In the table above,

        b is the bias term.
        w_i​ are the weights,.
        x_i​ are the input features.
        σ(z) is the activation function applied to z. In the case of logistic regression and many neural networks, the sigmoid function is commonly used as the activation function.

This equation above represents the transformation that occurs in a single neuron of a neural network. The linear part captures the weighted sum of input features, and the activation part introduces non-linearity to the model, allowing it to learn complex patterns in the data. This process is fundamental to the functioning of neural networks in tasks such as classification and regression.

With the sigmoid function, we can have,

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