d
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:
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?
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?
These are the histogram and Normal plot for the residuals, as shown in Answer 4:
5. What can we conclude from these distribution graphs?
This is the scatter plot of the residuals against the value predicted by the regression equation, as shown in Answer 4:
6. What can we conclude from the scatter diagram?
8. How could we check the assumption of linearity?
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Last updated: 20 March, 2007.
