2. 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 bwght; = Bo + Bicigsi + Befaminc +Ui, (1) where bwght is the baby birthweight in ounces; cigs is the number of cigarettes smoked per day while pregnant; and faminc is, yearly family income in thousands of dollars. (a) Do you think cigs and faminc are likely to be correlated? Explain why the correlation might be positive or negative. What is the most likely sign for B.? (b) We collect n = 1388 observations and we estimate the model in equation (1). We obtain the following results (Intercept) cigs faminc Estimate Std. Errort value 116.9741 1.0372 112.7780 -0.4634 0.0888 -5.2209 0.0928 0.0286 3.2451 Pr(>It) 0.0000 0.0000 0.0012 Everything else being equal, what is the effect of reducing cigs by 10 units on the weight of the baby at birth? (c) Construct a 95% confidence interval for Bi. (d) We would like now to test the null hypothesis that to offset the effect of one more cigarette smoked per day on birthweigth, family income should increase by $5000 a year. Write this null hypothesis using only the parameters and B2.
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