# Introduction

Ever wondered how it’s possible you can talk to your phone and it’s actually giving relevant answers?

The answer is: Neural networks. A computer technology which works very similar to the human brain. And makes it possible for computer software to learn from example data (data sets).

**How is this done?**

It’s not easy. In the end it’s all about statistics and statistical analysis. One specific statistical analysis technique is the most important: Regression analysis.

Imagine the following dataset, consisting of x and y values:

x-value | y-value |

5 | 10 |

10 | 20 |

15 | 30 |

20 | 40 |

25 | 50 |

30 | 60 |

Based on the data above, what would the y-value be when x = 18? The correct answer is: 36. Why?

Take a look at the data set and notice it’s simply doubling the data for x to get the y-value.

This is high school math and not very complicated.

We say y is a function of x.

In formula form: y=2x.

Now, let’s have a look at a real world example:

As you may notice, there’s no ‘fixed’ model. The data points are scattered around the real function. The function in this case is just a ‘best fit’ in the data set.

As you see, the function is a straight line. We therefore say it’s linear. This type of regression analysis is called ‘linear regression analysis’.

Below other ‘real world’ examples:

As you might see, the two examples above are non-linear. Both are plotted logarithmic. The number e, which is the base number for natural logarithms. By adjusting one or more of the axes to logarithmic is a common way of displaying logarithmic functions to display the functions in a nice way.

You may be able to think of even more complicated functions, such as quadratic, multi-dimensional or trigonometric. They all exist and are applied in machine learning.