If there is the equation,

Y = 2 * X + 3

,
Simulation is easy.

Example of simulation of this equation is

But real data is example below.
The data is near the simulated point above.

In statistical way, the eauation is

Y = 2 * X + 3 + E

The part "E" means "Error".
E is needed to evaluate dispersion.

In many models. E is omitted. But Structural Equation uses E usually.

The method to simulate the equation with E is the method in this page.

E is made from the randum numbers related with normal distribution.

sample file is the example.

Sample file uses 100 sets of data to study this method. But in my experience, more than 10000 sets of data is needed to take care of the precision of estimate and significant figures.

If the equation is complicated, the variation of this simulation is useful

For example, Prediction Interval and Error Analysis.

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Make Dispersion Data