4.7 Regression

Owned by Tessa Jacobs
Last updated: dec. 12, 2023 by Kor Oldenbroek
1 min read

But in case of a rather high correlation the question arises: How much change in y do you see with 1 unit change in x? That question can be answered by the regression coefficient: A measure of relation between x and y, but expressed as proportion the variance of x. It is usually denoted as b.

In statistical terms: b(x,y) =  cov (x,y) / (var x)2               

In words b(x.y) = is the change in the value of y when x is one unit higher. It is also possible to calculate the change in x when y is one unit higher.

That regression coefficient can be calculated as: b(y,x) = cov (x,y) / (var y)2

The regression coefficient can have a positive or a negative sign dependent on the sign of the correlation (covariance) between the traits. The regression coefficient, e.g. from daughter’s milk yield on dam’s milk yield can be used to estimate the heritability for milk yield.



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