In my previous posts, I explained the Linear Regression and stated that there are some errors in it. This is called the error or prediction (for individual predictions) and there is also a standard error. A prediction is good if the individual errors of prediction and the standard error are small. Let’s now start by examining the error of prediction.

## Error of prediction in Linear regression

Let’s recall the table from the previous tutorial:

Year | Ad Spend (X) | Revenue (Y) | Prediction (Y’) |

2013 | € 345.126,00 | € 41.235.645,00 | € 48.538.859,48 |

2014 | € 534.678,00 | € 62.354.984,00 | € 65.813.163,80 |

2015 | € 754.738,00 | € 82.731.657,00 | € 85.867.731,47 |

2016 | € 986.453,00 | € 112.674.539,00 | € 106.984.445,76 |

2017 | € 1.348.754,00 | € 156.544.387,00 | € 140.001.758,86 |

2018 | € 1.678.943,00 | € 176.543.726,00 | € 170.092.632,46 |

2019 | € 2.165.478,00 | € 199.645.326,00 | € 214.431.672,17 |

We can see that there is a clear difference in between the prediction and the actual numbers. We calculate the error in each prediction by taking the real value minus the prediction:

Y-Y’ |

-€ 7.303.214,48 |

-€ 3.458.179,80 |

-€ 3.136.074,47 |

€ 5.690.093,24 |

€ 16.542.628,14 |

€ 6.451.093,54 |

-€ 14.786.346,17 |

In the above table, we can see how each prediction differs from the real value. Thus it is our prediction error on the actual values.

## Calculating the Standard Error

Now, we want to calculate the standard error. First, let’s have a look at the formular:

Basically, we take the sum of all error to the square, divide it by the number of occurrences and take the square root of it. We already have Y-Y’ calculated, so we only need to make the square of it:

Y-Y’ | (Y-Y’)^2 |

-€ 7.303.214,48 | € 53.336.941.686.734,40 |

-€ 3.458.179,80 | € 11.959.007.558.032,20 |

-€ 3.136.074,47 | € 9.834.963.088.101,32 |

€ 5.690.093,24 | € 32.377.161.053.416,10 |

€ 16.542.628,14 | € 273.658.545.777.043,00 |

€ 6.451.093,54 | € 41.616.607.923.053,70 |

-€ 14.786.346,17 | € 218.636.033.083.835,00 |

The sum of it is: € 641.419.260.170.216,00

And N is 7, since it contains 7 Elements. Divided by 7, it is: € 91.631.322.881.459,50

The last step is to take the square root, which results in the standard error of € 9.572.425,13 for our linear regression.

Now, we have most items cleared for our linear regression and can move on to the logistic regression in our next tutorial.

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