Birth-weight data
Section of Linear model examples, part of Data analysis
Birth-weight data
| Type | Section |
| Taught in | Linear model examples |
| Part | Data analysis |
The birthwt data, in R’s MASS package, record 189 births. The response is the baby’s birth weight in grams; the explanatory variables include the mother’s age, her weight in pounds at her last menstrual period, her race (1 white, 2 black, 3 other), whether she smoked during pregnancy, and her history of hypertension and of uterine irritability.
Example 1 (Explaining birth weight) Question. Fit birth weight on the mother’s weight, age, race and smoking, and interpret each coefficient.
Solution.
library(MASS)
model1 <- lm(bwt ~ lwt + age + factor(race) + smoke, data = birthwt)
summary(model1)
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 2839.433 321.435 8.834 8.2e-16 ***
# lwt 4.000 1.738 2.301 0.02249 *
# age -1.948 9.820 -0.198 0.84299
# factor(race)2 -510.501 157.077 -3.250 0.00137 **
# factor(race)3 -398.644 119.579 -3.334 0.00104 **
# smoke -401.720 109.241 -3.677 0.00031 ***
# Residual standard error: 682.1 on 183 degrees of freedom
# Multiple R-squared: 0.1483, Adjusted R-squared: 0.125
# F-statistic: 6.373 on 5 and 183 DF, p-value: 1.758e-05The overall F test, p=1.8\times10^{-5}, says at least one of the variables is associated with birth weight. Taking them one at a time, each with the others held fixed:
- each extra pound of the mother’s weight goes with 4.0 g more birth weight on average (p=0.022);
- the mother’s age adds nothing once the other variables are known (p=0.84);
- babies of black mothers weigh 511 g less on average than those of white mothers, the reference level, and those of mothers of other races 399 g less (p=0.001 for both);
- babies of mothers who smoked weigh 402 g less than those of non-smokers of the same weight, age and race (p=0.0003).
The model explains only 15% of the variation in birth weight; the residual standard deviation is 682 g. These are observational data, so the coefficients are associations adjusted for the variables in the model, not effects: race, for instance, stands in for many unmeasured differences.