@AdamHart1
You ae right, in Insights, many of these statistics are behind each card which your viewers can visualize. If you run a regression model and predict variables then the regression model will have some statistics in its data table.
The predicted variable should include the predicted fields and residual value etc. You can open this dataset to check out their formulas
We mostly have the statistics related to the analysis displayed in the application and some of the other measures you may want to calculate on your own.
If you are using ArcGIS Insights desktop or Enterprise deployment you can choose to create these statistics by using data added in insights with Python & R module. You can then add them as a screenshot into the analysis.
Hope this helps.
Thanks,
Akshay Harshe