Given the modern day computing capabilities, calculating Image is easy . Here X and Y stand for dependent and independent variable data, the resultant computation gives the estimates of a linear model .

Below is Brunsviga Arithmometer, a tool for adding , subtracting, multiply and dividing. Yule, the famous statistician is known to have used 2 slide rules and this machine below to calculate betas.

Now, how does one one calculate inverse of a matrix using slide rule and arithmometer ? Truly amazing :). Think about the various issues in matrix inversion and one is amazed at the ways in which statisticians used mechanical devices to compute stuff.

Image

This barrel calculating machine represents the Brunsviga in its earliest form.
Barrel calculating machines were smaller, lighter and easier to operate than Arithmometers.
The machine performs multiplication by repeated addition and includes the wheel with a variable number of teeth as patented by
Willgodt T Odhner (1845-1905) in 1891.