How does excel calculate values when you drag out a range?

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I have been trying to find an answer online but haven't been able to find one.

When given a range of values, selecting this range and dragging out the cells will generate more values. How are these values calculated? In certain cases it is easy to figure, like when all values are the same or when they are increasing by a steady interval, but how are values calculated when more random sequences of values are given?

For example, given the range

Val 1 Val 2 Val 3 Val 4 Val 5 Val 6
5 5 6 54 5 2

when selecting all values and dragging out to the right, I will end up with the following range:

Val 1 Val 2 Val 3 Val 4 Val 5 Val 6 Dragged out 1 Dragged out 2 Dragged out 3
5 5 6 54 5 2 16.133 17.976 18.019

How are the three dragged out values calculated?

1 Answers

This is done using linear regression, as calculated by the least squares method, explained in this Wikipedia-article.

As an illustration, I have created an Excel sheet, containing the numbers from 1 to 6 and I've added your numbers. Then I've added the numbers 7-9 and used least squares method (as supported by Excel) and put everything in a graph. Please realise that the original values are shown but overwritten by the estimated values in the attached graph (the yellow cells contain the formula of the cell at its left):

enter image description here

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