Prediction of Child's Height

Birgit Kiesewetter
25 July 2016

Predict Child's Height

I recently heard that a girl must be between 174 und 182 cm high to become a model and the average height of basketball stars is around 2 m.

Wondering whether your offspring has a chance as model or basketball star?

'Predict Child's Height' is a nice small application to estimate your child height based on father's and mother's height. Try it out and enjoy!

- Click here to open the application -

The following 3 slides include some further information on the source and statistical model used.

Background Information

The data used to build this model is the 'GaltonFamilies' data set included in R package HistData. The data lists the individual observations for 934 children in 205 families from Galton's notebook. He used this data collection to analyse the relation between heights of parents and their offspring (1886).

This is the simple linear model created within R:

fit <- lm(childHeight ~ ., data=mydata)
coef(fit)

(Intercept)      father      mother  gendermale 
 44.0927768   0.4264473   0.2793852  14.5887217

From this model child's height will be calculated as given below:

  • For a Boy: \( 44.09 + 0.42 * Father + 0.28 * Mother + 1 * 14.59 \)
  • For a Girl: \( 44.09 + 0.42 * Father + 0.28 * Mother + 0 * 14.59 \)

Relation between Father's height and Child's height:

The figure below shows the relation of your Boy's or Girl's height based on Father's height only. For Mother's height we use the average with 163 cm. This results in the following formulas:
For a Boy: \( 44.09 + 0.42 * Father + 0.28 * 163 + 1 * 14.59 \)
For a Girl: \( 44.09 + 0.42 * Father + 0.28 * 163 + 0 * 14.59 \)

plot of chunk unnamed-chunk-3

Relation between Mother's height and Child's height:

The figure below shows the relation of your Boy's or Girl's height based on Mother's height only. For Father's height we use the average with 176 cm. This results in the following formulas:
For a Boy: \( 44.09 + 0.42 * 176 + 0.28 * Mother + 1 * 14.59 \)
For a Girl: \( 44.09 + 0.42 * 176 + 0.28 * Mother + 0 * 14.59 \)

plot of chunk unnamed-chunk-4