# Interactive statistics: breeding's equation AKA regression towards the mean

### An R shiny app for experimentation

One of the things I did to teach myself R programming was to create a bunch of interactive statistics tools written using the awesome R Shiny package. These are still online at the page for them. A few days ago, I was asked to produce one to showcase how regression towards the mean works, specially the breeder's equation. Dalliard has a long piece on regression towards the mean in general over at Human Varieties.

You can find the app here. Source code is public on Github. I don't think I can embed it here, but it looks like this. You plug in the assumed heritability, the grandparents and parents values of the phenotype of interest. The grandparent mean will be used as an estimate of the additive genetic mean of the population, so if you prefer that way, you can set them to the same value. I've plugged in some IQ-like numbers, but it should work equally well for any kind of metric. (Note that the calculations do not include any parent-to-child environmental transmission. If you think this is present, add it to the additive heritability to get a total family transmission variance share.)

## Interactive statistics: breeding's equation AKA regression towards the mean

So if I understand it correctly, the expected value of a child's IQ will be the simple average of mother's and father's IQ, plus a little scoop of regression in the direction of IQ 100 (the mean)?

Is this actually true? Is the (pre-regression) IQ of the children a simple arithmetic mean of the parents'?

Which value for "additive heritability" is realistic?

Also, and importantly, what is the standard deviation on said expected value of the children's IQ? I'd intuitively expect it to be a function of the gap between the mother's and the father's IQ. I.e. two people of IQ 120 are much less likely to give birth to an outlier, than say a couple combining IQ 90 and IQ 150. Do we have any statistical data and calculation method for this?

Cool. Thanks. Any other recommendations for teaching yourself R? About to jump into coding and looking for advice.