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A problem of interest to health officials (and others) is to determine the effects of smoking duringpregnancy 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 bepositive 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, focusingon whether adding faminc substantially changes the estimated effect of cigs on bwght.

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(i)Most likely sign for coefficient estimate of $\beta_{2}$ must be positive $( > 0),$ because more income for family typically means better nutrition for the mother and better prenatal care.(ii)An increase in income generally increases the consumption of a good. However cigs constitute small percentage of family income and it is relatively inelastic, therefore when faminc increases the share of cigarette consumption declines. It could be negatively correlated. The sample correlation between cigs and faminc is come out to be $-0.173,$ thus indicating a negative correlation.(iii).$ n =1,388 $$ R^{2} =0.030 $

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Chapter 3

Multiple Regression Analysis: Estimation

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Hi, everyone. We have the computer exciting chapter tree, and the problem is to determine the effects of smoking during pregnancy on infant Hells and we used the birth weight as a proxy for income tells, um, I mean question that we're interested in this one. Birth weight is equal to Betas Europe, plus beta long time cigarettes. Plants paid a two family income. Here, Bert Wait denounces Cigarette is demanding cigarettes smoked per day during pregnancy and family income using $1000. The question is what is the most likely signed for Beta two? And we already have a pill for that in the question for the last time. To see the question is higher income generally results in access to better prenatal care, as one is better nutrition from her mother. So from that, we would expect later to be positive. Would expect family income to have a positive effect on the in compounds, which is the boat right here keeping the moment. And the second question is, what do we think about the correlation between cigarettes and income is, do we expect them to be correlated? We would if we think that people have different consumption, different consumption behaviors in terms of smoking cigarettes when they have higher or lower incomes. If we think that cigarettes are normal, good. Stand with the thing that when people have higher incomes a gonna smoke more. That's would expect a positive correlation. What, actually, cigarettes, like a few year goods. So when family income goes up, people usually small class. So we expect. Okay, Negative correlation. So the males put this. So we expect data to be greater than zero. Right? And co ordination to be last year. Negative. Cornish. And the last question is, now you're gonna estimate these equations first using the income, then without the family income, and we're gonna compare our results. Okay, so we'll include some income. I get this estimate. So you stayed. I I just couldn't crest be Wait. Cigarettes, time income. And it gives me these estimates for Constant. My estimate is 116.97 for the effect of cigarettes. NATO, one hats, My estimate ISS negative points for six. And for the partial effect family income. My estimate is point Little night. We are squared from this regression is point or two 27 and sympathize is equal to 13 other than a cage. And when I run the regression without family income, I get the following guesstimate. So just a difference. She and I just got you killed her here to the estimate for the Karstens Now is 119 27 7 The my estimate full the effect of cigarettes beta, one pill days, negative 0.51. And your squad from this aggression. Actually, this was the squad room, second regression. And for the 1st 1 it wa ce point to 98. I'm just gonna correct this something about that and I emphasize it safe for two regressions. So first we're gonna discuss the results. That's Ah, look at this estimate from the first regression. So let's look a bit of what had first, this is points Make it a 0.46. Keeping family income fixed looking. One more cigarette today decreases the bird waiter innocent by 0.46 ounces. So when we look at the date, actually see that do you average cigarettes per day for the smokers is like 12. So this means that compared to a non smoker, smokers infant would have. So we just multiplied by 10 and we get Nick five from here. Right, please. 4.6. So this is for a smoker. Will have any contact ways. 4.6 ounces less dead compared to a from a nonsmoker. Okay. And, uh, so that's gonna be the two. Had that it was coming Incoming $1000. This means so if we put one here me is like a family having $2000. So this means that when the family come goes up by $1000 keeping Mr gets fixed. This means the difference is going away 0.9 more. All right, so the last thing we want to do is to compare. They know one had to battle him killed, compared the effective cigarettes on infant house when we include family income, too. When we do not include it. And we see that the difference in the coefficient is points. 05 brides. So again, we, uh, thankful. And ever smoker, the effect would be changing effect would be point off five times 10 assuming that have ever smoker smokes 10 cigarettes per day and this gives me 0.5 ounces is just a substantial difference. Well, you kind of know what is the average birth weight is and compare it to this. And when you go today, huh, you find that the average birch wage, it's like 120 hours is 118 or something like that. So this is like a change that is, in fact, less than 0.5%. Did that to me. Doesn't seem like much, but I don't really know much about Comptel. Make that difference is big, but I would say it's no much for big difference. Another obsession. Difference. All right, that is it for the question. Thank you for watching. That helps goodbye.

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