Question

3. (6 points) The dataset BWGT contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, the average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple OLS regression was estimated using data on n=1,388 births: bwgt = 119.77 – 0.514cigs What is the predicted birth weight when cigs=0? What about when cigs=20 (one pack per day)? Comment briefly on the difference. a. Does the simple regression above necessarily capture a causal relationship between the child's birth weight and the mother's smoking habits? Briefly explain why or why not. b. C. To predict a birth weight of 125 ounces, what would cigs have to be? Briefly comment on feasibility of your answer. d. The proportion of women in the sample who do not smoke while pregnant is about 0.85. Does this help reconcile your finding from part (c)? Briefly explain.

Answer 1

(a)

When cigs = 0, Birth weight = 119.77

When cigs = 20, Birth weight = 119.77 - 0.514 x 20 = 119.77 - 10.28 = 109.49

So, increase in smoking leads to lower birth weight.

(b)

The regression equation does not necessarily imply a causation, since birth weight depends on many other parameters on mother's health, habit, lifestyle and genetic factors, none of which is considered by the model.

(c)

125 = 119.77 - 0.514 x cigs

0.514 x cigs = - 5.23

cigs = - 10.18

Since number of cigarettes cannot be negative, this answer is not feasible.

(d)

If proportion of non-smoking expecting mothers is considered, the stated regression equation will not be valid and therefore, answer to (c) would be different.