We know that Correlation does not imply causation and in the same way, we also know that causation does not imply a linear correlation, however, for the sake of simplicy let's assume that our model is a simple linear regression model, then can I assume that my model implies causation if the correlation coefficient is equal 1?
In an excerpt I was reading they give an example of causation as below:
"Example of causality: First, you need to check if there is a correlation between the two variables, this is done with correlation analysis. If there is a significant correlation, the second condition must still be tested. The second condition can be confirmed either by theory or if there is a time sequence. In this case, there is a clear time sequence. If there is a correlation, it is clear that the variable "age at which the first sentence is spoken" influences the variable "later school success", the other way around is not possible."
Isn't the above example only an example of correlation? Since age only influences school success and doesn't cause it. A more formal way to paraphrase my question, in causality we know that Action A is always followed by Event B, and in the above example, this is not stated anywhere, so why is it an example of causation?