Words: 1505
The columns corresponds to bight (baby’s birthright measured in grams), smoker (equal to 1 if the mother smoked during pregnancy, O otherwise), gigs (average number of cigarettes smoked per day by the mother during pregnancy), medic (mothers education measured in years), natal (total number to antenatal [prior to birth] visits to a health professional), drink (average number of standard drinks of alcohol consumed per day during pregnancy), and page score (summary to intact health measured at birth, with values between O and 10).
Descriptive Statistics for the Sample (1) What is the average, minimum, and maximum value and standard deviation of child birthright, mother’s education, number of antenatal visits and page score in the BIGHT. RAW sample? Average minimum maximum standard deviation 3450. 7 Agog. C 4990. 0 493. 18 medic 13. 799 8. 0 17. 0 2. 0240 natal 11. 914 3. 0 36. 0 3. 9031 page 8. 3273 3. 010. 01. 0147 (2) What is the reggae number of cigarettes smoked per day for the sample ? What fraction Of the sample reported smoking during pregnancy (use the indicator variable smoker to determine this) ?
Among women who smoked, what is the average number of cigarettes smoked per day ? Given these values, is the sample average a good measure of the ‘typical” woman in this case ? Explain. The average number of cigarettes smoked per day for the sample (i. E. E[gigs]) is 1. 0036. The fraction of the sample that reported smoking (i. E. P rob[gigs > O] which is E[smoker]) is 0. 0935 or just over 9%. The average value of gigs for those who actually smoked (this is E[sigil gigs > O] = Elicits smoker)) = 1. 0036 0. 093525 – 10. 73.
Therefore the sample average gigs z 1 is not a good measure for the typical mother in the sample (since over do not smoke; and those that do smoke, typically smoke a lot more). bight 0+ p 1 gigs + u (3) In this model the coefficient O corresponds to the expected birthright of a child borne to a mother does not smoke. The coefficient 1 measures the difference in expected child birthright due to the mother smoking I additional cigarette per day on average during pregnancy, other things equal. (4) Estimate the simple regression model in (I) using the BIGHT.
RAW data and report the results in the standard form (i. E. Report coefficient estimates, standard errors, sample size, RE and RE statistics). Is gigs statistically significant (against a two-sided alternative) at the 5% level ? bight = 3467. 4 – 16. 657 gigs (30. 3) (7. 634) – n = 278, RE = 0. 0167, RE = 0. 0131 Simple Regression Model: Test – – Test Statistics: It’ SE(; -16. 657 1-2. 1651 2. 165. – 7. 6941 Rejection Rule: Reject HO in favor of HI if lit where t is the- statistic and c is the critical value for the t distribution with UDF 278 – 1 -1 -276 4 and a 5% significance level, Now lit = 2,165 and c= 1. , Decision: Since TTL > c we reject the null in favor of the alternative at the 5% level of significance. Conclusion: Cigarette consumption during pregnancy has a statistically significant effect on child birthright. HO : p 1 -O HI 1 6-0 (5) What is the predicted birth weight when gigs = 0 ? What is the predicted birth weight when gigs = 20 (one pack per day) ? 15 the difference practically large ? Briefly discuss. Predicted birth weight when gigs = 0 is bight = 3467. 4 – 16. 657 x O 3467. 4 grams. Predicted birth 3467_4 -?? 16. 657 x 20 3467. 4 – 333,14 = 3134. 26 grams.
The difference weight when gigs = 20 is bight in predicted birthright due to smoking an extra packet of cigarettes per day during pregnancy is 333. 14 grams (appear. One-third of a kilogram). To help gauge whether this difference is practically large or small, this amount corresponds to 333. 14 = 0. 0965 (or 3. 65%) of average child birthright in the sample. The 3450. 7 magnitude Of this is effect is practically large. (6) Does gigs explain most Of the variation in bight ? Does the model in (I) provide a good explanation of child birth weight ? Explain your reasoning.
The 2 for the model is only 0. 0167 ; so less than 2% of the variation in bight in the sample is explained by the model. Equivalently, over of the variation in bight remains unexplained. As an explanation of the determinants of child birth weight, this is not a good model, (7) Does the simple regression capture a causal relationship between the child’s birth weight and the mother’s smoking habits ? Explain. For the regression model to capture a causal relationship between mothers cigarette consumption and child birth weight, the critical condition that must be satisfied is the Zero
Conditional Mean (CM) assumption: I = O, V-actors not controlled for in the regression are in the error term, and these must be independent of gigs for the regression coefficient I to capture a causal or ‘cutters Paramus,’ effect, For instance, the average value of mothers overall health and nutrition, and access to antenatal care, must be same for all possible values of gigs (E[Lucia] = Oh These factors are likely to be correlated with cigarette consumption and therefore eve cannot interpret the model as capturing a causal effect of gigs on bight.
Multiple Regression Model – Estimation and Testing 8) Consider the model which includes additional characteristics of the mother (mother’s education) and use Of antenatal health services: bight = I gigs medic +;3 natal + u (2) Do you expect 3 to be positive or negative ? Provide one reason why 3 may be positive, and one reason Why ; 3 may be negative. Would expect ; 3 to be positive. A greater number of visits to a health professional is associated with more medical inputs and health care received during pregnancy, contributing to a healthier and heavier baby. This idea is a causal link – more health inputs leading to better health outcomes). However, it is possible if a mother has a difficult pregnancy, and there are complications, the mother may required additional medical 2 care. It this is the case, then ; 3 may be negative (the argument here is that of reverse causation – poor baby health and low bight leads to higher natal), (9) Estimate the model in (2) and report the results in the standard form. bight = 3187. 7 – 14. 761 gigs 2. 6952 medic 20. 197 natal (2283) (7_699) (1453) (7. 517) 22 – n = 278, R = 0. 0419, R = 0. 315 (10) Test the null hypothesis that natal has no impact on child birthright, other things equal, against a two-sided alternative using a 5% significance level. What do you conclude ? Test HO 3 = ВЇ ВЇ Test Statistics: I TTL = ВЇ SE(; -?? ВЇ 20. 197 – 7. 5173 Rejection Rule: Reject HO in favor of HI if lit where t is the t-statistic and c is the critical value for the t distribution With UDF = 274 * m, and a 5% significance level. Now lit = 2. 687 and c = 1. 96. Decision: Since lit > c we reject the null in favor Of the alternative at the 5% level Of significance.
Conclusion: The number of antenatal visits has a statistically significant effect on expected child birthright, other things equal. 11) Test the hypothesis that medic and natal are jointly insignificant in determining child birthright, holding gigs constant. Use a 1% significance level. Test: core Test Statistic: Or)/q – FAQ,n-k-1 – Our -k- 0. 0167) -0. 0419) ‘(278-4) 0. 0126 – 0. 0035 – 3. 6034 Rejection Rule: Reject HO in favor of HI if F > c, where c is the critical value for the distribution with UDF (2, 274) and a significance level.
Now 3. 6034 and c = 4. 61. Decision: Since c we do not reject the null in favor of the alternative at the 1% significance level. Conclusion: Based on the evidence in the ample, mothers education and number of antenatal visits are jointly insignificant in explaining child birthright, when cigarette consumption is held constant. (12) Another health risk factor that may influence child birthright is the mother’s consumption Of alcohol during pregnancy. What is the correlation between gigs and drinks in the sample ?
If drinks does have an impact on child birthright, What is the effect Of omitting this explanatory variable from the model in (2) ? Explain. The correlation between gigs and drinks in the sample is 0. 32. If drinks does have an impact on child birth weight (e. . The coefficient on drinks, 13 4 6= O), then omitting this variable from the model will lead 3 to ‘omitted variable bias. ‘ The LOS estimator for the model in (2) will be biased; the estimates will be misleading and the inference based on the results will be wrong.
Decision: Since F > c we reject the null in favor of the alternative at the 1% significance level. Conclusion: The model has statistically significant explanatory power. (20) Based on the estimation results for models (IHA), hat do you conclude regarding the causal effect of a mother’s smoking during pregnancy on the health of her child at birth ? Explain the reasons for your conclusions. Note: the most important aspect of answers to this questions is the presentation of a reasoned discussion based on the estimation results presented for the project.
It is acceptable to argue there is a significant negative health effect, no significant health impact, or even the conclusion that nothing can be learned trot the estimation – so long as an argument is made based on the evidence from the models estimated. The model estimation results must be retorted to in the discussion. Plus there must be a discussion of whether the CM is likely to hold in each / any model (the CM assumption is essential for the estimator to be measuring a causal effect).