Question

A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various illnesses. Since factors other than cigarette smoking that affect birth weight are likely to be correlated with smoking, we should take those factors into account. For example, higher income generally results in access to better prenatal care, as well as better nutrition for the mother. An equation that recognizes this isbwght = β0+β1cigs +β2 faminc + u.(i) What is the most likely sign for β2?(ii) Do you think cigs and faminc are likely to be correlated? Explain why the correlation might be positive or negative.(iii) Now, estimate the equation with and without faminc, using the data in BWGHT .RAW. Report the results in equation form, including the sample size and R-squared. Discuss your results, focusing on whether adding faminc substantially changes the estimated effect of cigs on bwght.

Answer 1

In studying the effects of smoking during pregnancy on birth weight, higher family income is likely to have a positive effect (positive β2), while the correlation between smoking and income could be negative but requires empirical testing. Including family income in the estimation could significantly alter the estimated effect of smoking on birth weight.

Step-by-step explanation:

When examining the impact of smoking during pregnancy on infant health and specifically birth weight, it is crucial to take into account various confounding factors. The equation of interest is bwght = β0+β1cigs +β2faminc + u, where bwght represents birth weight, cigs represents the number of cigarettes smoked, and faminc represents family income.

(i) The most likely sign for β2 is positive, since higher family income is generally associated with better prenatal care and nutrition, leading to healthier birth outcomes.

(ii) The correlation between cigs and faminc might be negative, as higher income families generally have better access to health education and resources, potentially leading to lower smoking rates. However, this is an empirical question and should be tested with data.

(iii) Estimating the equation with and without the variable faminc using the BWGHT.RAW dataset would provide insights into the effects of cigarette smoking on birth weight while controlling for family income. We anticipate that including faminc could alter the coefficient of cigs, suggesting that some of the effect of smoking on birth weight might be related to socioeconomic factors like family income.