3. On average a baby born with a low birth weight is more likely to have health
ID: 3305100 • Letter: 3
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3. On average a baby born with a low birth weight is more likely to have health problems. According to the Centers for Disease Control (CDC): "Smoking during pregnancy can cause a baby to be born too early or to have low birth weight." Suppose you are trying to uncover the relationship between the number of cigarettes smoked per day by pregnant mothers and the birth weight of their babies. Use the dataset called PS2_BWGHT.dta (see instructions at the end of the problem set for opening the dataset), to regress birth weight (variable bwght) against the number of cigarettes smoked per day (variable cigs) a. The results follow the sample regression line: bwght Acigs To do this in STATA, use the following command regress bwght cigs. What is the interpretation of B1, the estimated coefficient on cigs that you calculated with STATA? [HINT: Use the describe command to find out the units of the two variables] b. Do you think the zero conditional mean assumption is satisfied in the model that was estimated in part (a)? In other words, does E(vlcigs) E(v) = 0 ? Explain in 2-3 sentences. Family income is a factor that we omitted from the model in part (a). The model should have been c. In part (a) we omitted this relevant variable. Do you think this resulted in the estimate of ß in part (a) being biased? If so, in what direction do you think it was biased? [HINT: Use the table on the bottom of page 90 that we discussed in class] d. EXTRA CREDIT. Luckily, family income is in the dataset. Try running the model controlling for family income. How does the new estimated coefficient on cigs differ from what you calculated in part (a), and does this agree with your prediction in part (c)?Explanation / Answer
Rolling a single die
1) probability of rolling divisors of 6 :
Since its a single die, the possible outcomes are 1,2,3,4,5,6. All have equal probability(1/6) since its a fair die
Out of these divisors of 6 are 1,2,3,6. So P(divisors of 6) = 1/6*1/6*1/6*1/6 = 1/1296 = 0.0008
2) probability of rolling a multiple of 1: Since all(1,2,3,4,5,6) are multiples of 6 = 1/6*1/6*1/6*1/6*1/6*1/6= 1/46656 = 0.00002
3) probability of rolling an even number : There are 3 even numbers between 1-6 i.e. 2,4,6
Hence probability of rolling an even number = 1/6*1/6*1/6 = 1/216 =0.0046
4) List of all possible outcomes of rolling a single die ={1,2,3,4,5,6}
5) probability of rolling factors of 3 : Factors of 3 are 1,3
Hence probability of rolling factors of 3 = 1/6*1/6 = 1/36 = 0.0278
6) probability of rolling a 3 or smaller : 3 or smaller are 1,2,3. Hence the probability = 1/6*1/6*1/6 = 1/216 = 0.0046
7) probability of rolling a prime number: Prime numbers between 1-6 are 2,3,5 hence probability = 1/6*1/6*1/6=1/216=0.0046
8) probability of rolling factors of 4 : Factors of 4 are 1,2,4 hence the probability = 1/6*1/6*1/6 = 1/216 =0.0046
9) probability of rolling divisors of 30 : Divisors of 30 are 1,2,3,5,6 = 1/6*1/6*1/6*1/6*1/6 = 1/7776 = 0.0001
10) probability of rolling factors of 24: Factors of 24 are 1,2,3,4,6 = 1/6*1/6*1/6*1/6*1/6=1/7776=0.0001
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