There may be genetic variants that cause low birthweight and also contribute to risk of chronic disease. The DAG below captures this extra relationship. Should we now adjust for birthweight in analysing for a potential relationship between maternal smoking and chronic disease in the offspring?
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Putting It Together: Smoking and Birth Weight It is well known that women should not smoke while pregnant, but what is the effect of smoking on a baby's birth weight? Researchers Ira M. Bernstein and associates "sought to estimate how the pattern of maternal smoking throughout pregnancy influences newborn size." To conduct this study, 160 pregnant, smoking women were enrolled in a prospective study. During the third trimester of pregnancy, the woman self-reported the number of cigarettes smoked. Urine samples were collected to measure cotinine levels (to assess nicotine levels). Birth weights (in grams) of the babies were obtained upon delivery. Source: Ira M. Bernstein et. al. "Maternal Smoking and Its Association with Birthweight." Obstetrics \& Gynecology 106 (Part 1) 5,2005 . (a) The histogram on the next page, drawn in Minitab, shows the birth weight of babies whose mothers did not smoke in the third trimester of pregnancy (but did smoke prior to the third trimester). Describe the shape of the distribution. What is the class width of the histogram? (b) Is this an observational study or a designed experiment? (c) What does it mean for the study to be prospective? (d) Why would the researchers conduct a urinalysis to measure cotinine levels? (e) What is the explanatory variable in the study? What is the response variable? Is the explanatory variable qualitative or quantitative? Is the response variable qualitative or quantitative? (f) The scatter diagram of the data drawn using Minitab is shown below. What type of relation appears to exist between cigarette consumption in the third trimester and birth weight? (g) Use the regression output from Minitab to report the leastsquares regression line between cigarette consumption and birth weight. Regression Analysis: BirthWeight versus Cigarettes $$\begin{array}{rrrr}\text{The regression equation is }\\ \text{BirthWeight } =3456-31.0 \text{ Cigarettes } \end{array}$$ $$\begin{array}{rrrr}\text{ Predictor } \quad \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text{ Constant } \quad 3456.04 & 45.44 & 76.07 & 0.000 \\ \text{ Cigarettes } \quad-31.014 & 6.498 & -4.77 & 0.000\end{array}$$ $$S=482.603 \quad \mathrm{R}-\mathrm{Sq}=12.6 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{adj})=12.0 \mathrm{~s}$$ (h) Interpret the slope. (i) Interpret the $y$ -intercept. (j) Would you recommend using this model to predict the birth weight of a baby whose mother smoked 10 cigarettes per day during the third trimester? Why? (k) Does this study demonstrate that smoking during the third trimester causes lower-birth-weight babies? (I) Cite some lurking variables that may confound the results of the study.
Describing the Relation between Two Variables
Least-Squares Regression
It is well known that women should not smoke while pregnant, but what is the effect of smoking on a baby's birth weight? Researchers Ira M. Bernstein and associates "sought to estimate how the pattern of maternal smoking throughout pregnancy influences newborn size." To conduct this study, 160 pregnant, smoking women were enrolled in a prospective study. During the third trimester of pregnancy, the woman self-reported the number of cigarettes smoked. Urine samples were collected to measure cotinine levels (to assess nicotine levels). Birth weights (in grams) of the babies were obtained upon delivery. Source: Ira M. Bernstein et. al. "Maternal Smoking and Its Association with Birth-weight." Obstetrics \& Gynecology 106 (Part 1) 5, 2005. (a) The histogram, drawn in MINITAB, shows the birth weight of babies whose mothers did not smoke in the third trimester of pregnancy (but did smoke prior to the third trimester). Describe the shape of the distribution. What is the class width of the histogram? (b) Is this an observational study or a designed experiment? (c) What does it mean for the study to be prospective? (d) Why would the researchers conduct a urinalysis to measure cotinine levels? (e) What is the explanatory variable in the study? What is the response variable? (f) The scatter diagram of the data drawn using MINITAB is shown on the next page. What type of relation appears to exist between cigarette consumption in the third trimester and birth weight? (g) Use the regression output from MINITAB to report the least-squares regression line between cigarette consumption and birth weight. (h) Interpret the slope. (i) Interpret the $y$ -intercept. (j) Would you recommend using this model to predict the birth weight of a baby whose mother smoked 10 cigarettes per day during the third trimester? Why? (k) Does this study demonstrate that smoking during the third trimester causes lower-birth-weight babies? (l) Cite some lurking variables that may confound the results of the study. (GRAPH CAN'T COPY)(FIGURE CAN'T COPY)
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 is $$=\beta_{0}+\beta_{1} \text { cigs }+\beta_{2} \text { faminc }+u$$ (i) What is the most likely sign for $\beta_{2} ?$ (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. Report the re- sults 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.
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