# Exercise: Head circumference, sex, and height

We have already seen that male students had a significantly bigger mean head circumference than female students (Week 4 Exercise: Head circumference) and also that, for females, head circumference and height were related (Week 7 Exercise: Head circumference and height). Could it be that the difference in head circumference between the sexes is explained by the difference in height?

The following graph shows a plot of head circumference against height for males and females:

## Questions

1. What method could we use to answer the question: is the difference in head circumference between the sexes explained by the difference in height?

The regression equation is

Head (mm) = 396 + 0.0957 × height (mm) + 6.80 × sex

where sex = 1 for a female, 2 for a male.

2. What does 6.80 tell us?

We can add confidence intervals and P values for the coefficients in this equation:

Head (mm)   =   396     +     0.0957 × height (mm)     +     6.80 × sex
95% CI                         334 to 459   0.0555 to 0.1360                   -1.1 to 14.6
P<0.001             P<0.001                           P=0.09

3. What can we conclude from this analysis?