can a perceptron be used for regression?
The deep feedforward neural networks used for regression are nothing but multilayer perceptron architectures.



Originally, perceptrons were used as binary classifiers i.e to classify binary labels ( 0 or 1 ). But, if no non-linear activation function is applied to the dot product of the features and weights, then it is simply a linear regressor.

If the linear function is $f(x) = x$ and $N$ is the number of features then,

$\Large y = \sum_{i=0}^N x_i w_i$

or using vector notation,

$\Large y = \vec{x}.\vec{w} ...(1)$

For multiple regression, we use the below equation with mean-squared error loss function to optimize the $\beta$ parameters,

$\Large y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 ... \beta_n X_n$

Let , 

$\Large 
\vec{W} = [ \beta_1 \ \beta_2 \ \beta_3 \ ... \ \beta_n ] \\
\vec{X} = [ X_1 \ X_2 \ X_3 \ ... \ X_n ]
$ 

Where $N$ is the number of features, $\vec{X}$ is the feature vector and $\vec{W}$ is the weights vector. Then, 

$\Large y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 ... \beta_n X_n = \beta_0 + \vec{W}.\vec{X} ...(2) $

Where, $\beta_0$ is also called as the bias coefficient in Artificial Neural Networks. You can relate equations 1 and 2 and understand the concept.


  Hence, $\Large y = \vec{x}.\vec{w} + bias $ generally represents a hyperplane
  which is used in linear regression.