Implementing a basic neural network from scratch and comparing it with Scikit-Learn's MLP Regressor.

Study 1: Basic performance comparison In this study we compare basic stochastic gradient descent with a similar implementation of Sklearn. Sklearn outperforms due to inherent optimizations in implementation.

Study 2: Comparison of dataset size against performance Sklearn takes more time due to persistent search for optimum solution.

Study parameters:

1. Sigmoid activation function
2. One input layer with three features
3. One hidden layer with four neurons
4. One output layer (regression task)