Linear Regression and Perceptron

 - Neural Network Nodes (Perceptron)

A neural network node, also called a neuron or perceptron, is a computational unit with one or more weighted input connections, a transfer function that combines the inputs in some way, and an output connection. The nodes are then organized into layers to form the network. 

Think of each individual node as its own linear regression model, consisting of input data, weights, biases (or thresholds), and outputs. The formula looks like this:  

Mathematical formula used to determine summation:

∑wixi + bias = w1x1 + w2x2 + w3x3 + bias

Mathematical formula used to determine the output:

output = f(x) = 1 if ∑w1x1 + b>= 0; 0 if ∑w1x1 + b < 0

Once the input layer is determined, weights are assigned. These weights help determine the importance of any given variable, with larger variables contributing more to the output than other inputs. All inputs are then multiplied by their respective weights and summed. 

After that, the output is passed through an activation function, which determines the output. If that output exceeds a given threshold, it "triggers" (or activates) the node, passing the data to the next layer in the network. 

This causes the output of one node to become the input of the next node. This process of passing data from one layer to the next defines the neural network as a feedforward network. 

Please refer to Wikipedia: Perceptron for more details.

- Linear Regression 

Linear regression analysis is used to predict the value of one variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you use to predict the value of another variable is called the independent variable. 

This form of analysis estimates the coefficients of a linear equation involving one or more independent variables that best predict the value of the dependent variable. 

Linear regression fits a line or surface to minimize the difference between predicted and actual output values. 

There are some simple linear regression calculators that use the "least squares" method to find the line of best fit for a set of paired data. Then, you estimate the value of X (dependent variable) based on Y (independent variable).