Correlation

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I have used the term to mean different things and I have used different symbols.

"Heritability can be estimated from phenotypic correlations as a function of relationship."

Here, I used the term in the general sense of the dependency of the offspring phenotypic value upon the offspring value.  This dependency can be measured as the slope of a graph or as Pearson's correlation coefficient (tightness of the graph).

"Pearson's correlation coefficient"

The fraction of the variance that varies jointly in two sets of data (covariance compared with variances).

Normally denoted by r, but in our context, we used the letter t to distinguish it from relationship.

Can be used to estimate heritability (t/r).

"Slope (b)"

The slope is the dependency of the offspring mean on the parental mean.