Medical researchers have noted that adoles­cent females are much more likely to deliver low birth weight babies than are adult females. Because low birth weight babies have a higher mortality rate, a number of studies have examined the relationship between birth weight and mother’s age. One such study is described in the article “Body Size and Intelligence in 6 Year Olds: Are Offspring of Teenage Mothers at Risk?”(Maternal and Child Health Journal [2009]: 847– 856). The following data on maternal age (in years) and birth weight of baby (in grams) are consistent with summary values given in the article and also with data published by the National Center for Health Statistics.
Mother’s age………………….. 15 17 18 15 16 19
Birth weight ………………….. 2289 3393 3271 2648 2897 3327
Mother’s age………………….. 17 16 18 19
Birth weight………………….. 2970 2535 3138 3573
a. If the goal is to learn about how birth weight is related to mother’s age, which of these two variables is the response variable and which is the predictor variable?
b. Construct a scatterplot of these data. Would it be reasonable to use a line to summarize the relationship between birth weight and mother’s age?
c. Find the equation of the least squares regression line.
d. Interpret the slope of the least squares regression line in the context of this study.
e. Does it make sense to interpret the intercept of the least squares regression line? If so, give an interpretation. If not, explain why it is not appropriate for this data set.
f. What would you predict for birth weight of a baby born to an 18 year old mother?
g. What would you predict for birth weight of a baby born to a 15 year old mother?
h. Would you use the least squares regression equation to predict birth weight for a baby born to a 23 year old mother? If so, what is the predicted birth weight? If not, explain why.