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Here are the problems for Stata preferably but other program is also fine.

(#4) birthweight2.dta contains information, for a sample of 1,719 infants, on infant birth weight (in grams), Apgar scores, demographic characteristics, and health behaviors of the mother. For this problem, both the Stata code and output are given. You may reproduce it if you wish, but to receive credit, you only need to answer the questions interpret the results. (You are NOT required to turn in a do-file, log-file, or graphs with this question. You may write your answers concisely on a separate page to minimize the number of pages in your upload file.) (a) Consider the relationship between mother’s age (mage) and baby birthweight (bwght). To start, use Stata’s twoway graph command to make a scatter plot along with the best fitting quadratic curve. Stata notes. Recall that to graph a scatter plot combined with the OLS fitted line, you would type: . twoway (scatter bwght mage) (1fit bwght mage) To fit a quadratic model and graph it with the scatter plot, simply replace 1£it with qfit: . twoway (scatter bwght mage) (qfit bwght mage) 3000 4000 5000 2000 1000 0 10 20 30 40 50 mother's age, years ® birth weight, grams Fitted values (b) Suppose you were to estimate the model for birthweight that includes both mage and its square: bwght = Bo + P1mage + Pamagesq +u Question: Based on the figure in (a), what sign would you expect to find for B 1? For B 2? (c) Estimate the model and check your answer to (b). (You will first need to create the variable magesq.) . gen magesq = mage“2 . reg bwght mage magesq Source | ss af MS Number of obs = 1,719 + ———- ——e- -- F(2, 1716) = 6.41 Model | 4028142.24 2 2014071.12 Prob > F = 0.0017 Residual | 538877828 1,716 314031.368 R-squared = 0.0074 + ——- - Adj R-squared = 0.0063 Total | 542905970 1,718 316010.46 Root MSE 560.39 bwght | Coef. Std. Err. t >t] [95% Conf. Interval] mmm Hmmm mmm mm mmm - meee mage | 85.94993 26.10133 3.29 0.001 34.75616 137.1437 magesq | -1.363882 .4372561 -3.12 0.002 -2.221493 -.506271 cons | 2094.667 384.6388 5.45 0.000 1340.256 2849.077 Question: Is the squared term statistically significant? (d) To get a better visualization of the parabola, create the predicted values from your regression in (b). Recall that the relevant command (following a regress command) is: . predict yhat (where yhat is the name of the variable that will contain the predicted or “fitted” values). Then create a scatter plot of the fitted values (yhat) against mage. . scatter yhat mage Questions: Is the turning point in this parabola empirically relevant (are there observations in the range of values above and below it)? What is the (approx..) mother’s age that “maximizes” birthweight (in a non- causal sense)? g 3400 8 s . . £8 ° . 33 E . . & . . 8 . 8 . . 8 5 10 20 30 40 50 mother's age, years (e) Now consider the effect of maternal cigarette smoking and pre-natal doctor visits on the infant’s birthweight. Estimate a model that includes the dummy variable for whether the mother smoked during pregnancy (msmoke) and the dummy for mothers who had at least 10 prenatal doctor’s visits (prenat10). Also include the interaction of these two dummy variables. (You will need to create the interaction variable msmokeXpn10.) Report the results. bwght = Bo + B1 msmoke + Pz prenatl0 + Bs msmokeXpnl0 + u . gen msmokeXpnl0 = msmoke*prenat10 . reg bught msmoke prenatl0 msmokeXpnl0 source | ss af Ms Number of obs = 1,719 - F(3, 1715) = 13.08 Model | 12140359.8 3 4046786.6 Prob > F = 0.0000 Residual | 530765611 1,715 309484.321 R-squared = 0.0224 ————————— #mmmmmmmmmmmmmmmmeem—eeee—ee———--—- Adj R-squared = 0.0207 Total | 542905970 1,718 316010.46 Root MSE = 556.31 | + msmoke | -312.1553 71.0471 -4.39 0.000 -451.5035 -172.8072 prenatl0 | 87.44224 30.22545 2.89 0.004 28.15961 146.7249 msmokeXpnl0 | 208.1915 96.71639 2.15 0.031 18.49702 397.886 _cons | 3371.47 25.02971 134.70 0.000 3322.378 3420.562 (f) Use the coefficients from the model you estimated in (e) to calculate the following (round to nearest gram): ® The predicted infant birthweight for mothers who smoked and had >10 prenatal visits: * The predicted infant birthweight for mothers who smoked and had <10 prenatal="" visits:="" *="" the="" predicted="" infant="" birthweight="" for="" mothers="" who="" did="" not="" smoke="" and="" had=""><10 prenatal="" visits:="" ®="" the="" predicted="" effect="" of="" smoking="" on="" infant="" birthweight="" for="" mothers="" with="">10 prenatal visits: ® The predicted effect of smoking on infant birthweight for mothers with <10 prenatal="" visits:="" ®="" the="" predicted="" difference="" in="" infant="" birthweights="" between="" mothers="" with="">10 prenatal visits and those with <10 prenatal="" visits="" (i.e.="" the="" predicted="" effect="" of="" prenat10)="" among="" mothers="" who="" smoke:="" *="" give="" two="" interpretations="" of="" the="" coefficient="" on="" msmokexpnl10.="" what="" does="" it="" represent?="" (g)="" control="" linearly="" for="" mage="" in="" the="" regression="" from="" part="" (e).="" .="" reg="" bwght="" mage="" msmoke="" prenatl0="" msmokexpnl0="" source="" |="" ss="" af="" ms="" number="" of="" obs="1,719" ———="" -="" --="" f(4,="" 1714)="10.07" model="" |="" 12467834.6="" 4="" 3116958.64="" prob=""> F = 0.0000 Residual | 530438136 1,714 309473.825 R-squared = 0.0230 — -- Adj R-squared = 0.0207 = 556.3 316010.4 Root MSE t P>|t| [95% Conf. Interval] mage | 2.938795 2.856882 1.03 0.304 ~-2.664548 8.542138 msmoke | -308.2923 71.14508 -4.33 0.000 -447.8326 -168.7519 prenatl0 | 84.53738 30.35657 2.78 0.005 24.99756 144.0772 msmokeXpnl0 | 207.6462 96.7162 2.15 0.032 17.95194 397.3404 _cons | 3286.328 86.47028 38.01 0.000 3116.729 3455.926 Question: Should we conclude that mother’s age has no significant effect on birthweight once we control for smoking and prenatal visits? (h) Suppose you are interested in whether the effect of prenatal visits on birthweight differs by infant gender, and you estimate the following regression: . gen prenatlOXmale = prenatlO+male . reg bught mage magesq prenatl0 prenatlOXmale Source | ss af MS Number of obs = 1,719 BE — - -- F(4, 1714) 8.33 Model | 10355821.3 4 2588955.33 Prob > F = 0.0000 Residual | 532550149 1,714 310706.038 R-squared 0.0191 — - -- Adj R-squared = 0.0168 1,718 316010.4 Root MSE = 557.41 std. Err. t >t] [95% Conf. Interval] 79.50583 26.03277 3.05 0.002 28.44648 130.5652 nage | magesq | =-1.270711 .4357605 -2.92 0.004 -2.12539 -.4160328 prenatl0 | 69.59221 33.37728 2.09 0.037 4.127718 135.0567 prenatlOXmale | 79.16406 32.82891 2.41 0.016 14.77511 143.553 _cons | 2127.88 382.8444 5.56 0.000 1376.988 2878.772 Question: Should you conclude that the effect of prenat10 is significantly larger for male babies? ‘Why or why not? (i) Finally, consider the relationship between an infant's Apgar score at one minute (apgarlm) and the average number of cigarettes the mother smoked per day (cigs). Suppose you estimate the following regression with cigs in quadratic form: . gen cigsq = cigs"2 . reg apgarlm cigs cigsq Source | ss af MS Number of obs = 1,719 mmm Heme ee —---- F(2, 1716) = 3.99 Model | 9.8077019 2 4.90385095 Prob > F = 0.0186 Residual | 2107.61405 1,716 1.22821332 R-squared = 0.0046 + - ----- Adj R-squared = 0.0035 | 1.23249229 Root MSE = 1.1082 | Interval] [eel ieimro Ammen — cigs | -.0276565 .016572 -1.67 0.095 -.06016 .004847 | .0004735 .0007048 0.67 0.502 -.0009089 0018558 | 8.402203 .0278036 302.20 0.000 8.347671 8.456736 Question: Should you conclude that there is no significant relationship between cigarette smoking and apgarIm?

(#4) birthweight2.dta contains information, for a sample of 1,719 infants, on infant birth weight (in grams), Apgar scores, demographic characteristics, and health behaviors of the mother. For this problem, both the Stata code and output are given. You may reproduce it if you wish, but to receive credit, you only need to answer the questions interpret the results. (You are NOT required to turn in a do-file, log-file, or graphs with this question. You may write your answers concisely on a separate page to minimize the number of pages in your upload file.) (a) Consider the relationship between mother’s age (mage) and baby birthweight (bwght). To start, use Stata’s twoway graph command to make a scatter plot along with the best fitting quadratic curve. Stata notes. Recall that to graph a scatter plot combined with the OLS fitted line, you would type: . twoway (scatter bwght mage) (1fit bwght mage) To fit a quadratic model and graph it with the scatter plot, simply replace 1£it with qfit: . twoway (scatter bwght mage) (qfit bwght mage) 3000 4000 5000 2000 1000 0 10 20 30 40 50 mother's age, years ® birth weight, grams Fitted values (b) Suppose you were to estimate the model for birthweight that includes both mage and its square: bwght = Bo + P1mage + Pamagesq +u Question: Based on the figure in (a), what sign would you expect to find for B 1? For B 2? (c) Estimate the model and check your answer to (b). (You will first need to create the variable magesq.) . gen magesq = mage“2 . reg bwght mage magesq Source | ss af MS Number of obs = 1,719 + ———- ——e- -- F(2, 1716) = 6.41 Model | 4028142.24 2 2014071.12 Prob > F = 0.0017 Residual | 538877828 1,716 314031.368 R-squared = 0.0074 + ——- - Adj R-squared = 0.0063 Total | 542905970 1,718 316010.46 Root MSE 560.39 bwght | Coef. Std. Err. t >t] [95% Conf. Interval] mmm Hmmm mmm mm mmm - meee mage | 85.94993 26.10133 3.29 0.001 34.75616 137.1437 magesq | -1.363882 .4372561 -3.12 0.002 -2.221493 -.506271 cons | 2094.667 384.6388 5.45 0.000 1340.256 2849.077 Question: Is the squared term statistically significant? (d) To get a better visualization of the parabola, create the predicted values from your regression in (b). Recall that the relevant command (following a regress command) is: . predict yhat (where yhat is the name of the variable that will contain the predicted or “fitted” values). Then create a scatter plot of the fitted values (yhat) against mage. . scatter yhat mage Questions: Is the turning point in this parabola empirically relevant (are there observations in the range of values above and below it)? What is the (approx..) mother’s age that “maximizes” birthweight (in a non- causal sense)? g 3400 8 s . . £8 ° . 33 E . . & . . 8 . 8 . . 8 5 10 20 30 40 50 mother's age, years (e) Now consider the effect of maternal cigarette smoking and pre-natal doctor visits on the infant’s birthweight. Estimate a model that includes the dummy variable for whether the mother smoked during pregnancy (msmoke) and the dummy for mothers who had at least 10 prenatal doctor’s visits (prenat10). Also include the interaction of these two dummy variables. (You will need to create the interaction variable msmokeXpn10.) Report the results. bwght = Bo + B1 msmoke + Pz prenatl0 + Bs msmokeXpnl0 + u . gen msmokeXpnl0 = msmoke*prenat10 . reg bught msmoke prenatl0 msmokeXpnl0 source | ss af Ms Number of obs = 1,719 - F(3, 1715) = 13.08 Model | 12140359.8 3 4046786.6 Prob > F = 0.0000 Residual | 530765611 1,715 309484.321 R-squared = 0.0224 ————————— #mmmmmmmmmmmmmmmmeem—eeee—ee———--—- Adj R-squared = 0.0207 Total | 542905970 1,718 316010.46 Root MSE = 556.31 | + msmoke | -312.1553 71.0471 -4.39 0.000 -451.5035 -172.8072 prenatl0 | 87.44224 30.22545 2.89 0.004 28.15961 146.7249 msmokeXpnl0 | 208.1915 96.71639 2.15 0.031 18.49702 397.886 _cons | 3371.47 25.02971 134.70 0.000 3322.378 3420.562 (f) Use the coefficients from the model you estimated in (e) to calculate the following (round to nearest gram): ® The predicted infant birthweight for mothers who smoked and had >10 prenatal visits: * The predicted infant birthweight for mothers who smoked and had <10 prenatal="" visits:="" *="" the="" predicted="" infant="" birthweight="" for="" mothers="" who="" did="" not="" smoke="" and="" had=""><10 prenatal="" visits:="" ®="" the="" predicted="" effect="" of="" smoking="" on="" infant="" birthweight="" for="" mothers="" with="">10 prenatal visits: ® The predicted effect of smoking on infant birthweight for mothers with <10 prenatal="" visits:="" ®="" the="" predicted="" difference="" in="" infant="" birthweights="" between="" mothers="" with="">10 prenatal visits and those with <10 prenatal="" visits="" (i.e.="" the="" predicted="" effect="" of="" prenat10)="" among="" mothers="" who="" smoke:="" *="" give="" two="" interpretations="" of="" the="" coefficient="" on="" msmokexpnl10.="" what="" does="" it="" represent?="" (g)="" control="" linearly="" for="" mage="" in="" the="" regression="" from="" part="" (e).="" .="" reg="" bwght="" mage="" msmoke="" prenatl0="" msmokexpnl0="" source="" |="" ss="" af="" ms="" number="" of="" obs="1,719" ———="" -="" --="" f(4,="" 1714)="10.07" model="" |="" 12467834.6="" 4="" 3116958.64="" prob=""> F = 0.0000 Residual | 530438136 1,714 309473.825 R-squared = 0.0230 — -- Adj R-squared = 0.0207 = 556.3 316010.4 Root MSE t P>|t| [95% Conf. Interval] mage | 2.938795 2.856882 1.03 0.304 ~-2.664548 8.542138 msmoke | -308.2923 71.14508 -4.33 0.000 -447.8326 -168.7519 prenatl0 | 84.53738 30.35657 2.78 0.005 24.99756 144.0772 msmokeXpnl0 | 207.6462 96.7162 2.15 0.032 17.95194 397.3404 _cons | 3286.328 86.47028 38.01 0.000 3116.729 3455.926 Question: Should we conclude that mother’s age has no significant effect on birthweight once we control for smoking and prenatal visits? (h) Suppose you are interested in whether the effect of prenatal visits on birthweight differs by infant gender, and you estimate the following regression: . gen prenatlOXmale = prenatlO+male . reg bught mage magesq prenatl0 prenatlOXmale Source | ss af MS Number of obs = 1,719 BE — - -- F(4, 1714) 8.33 Model | 10355821.3 4 2588955.33 Prob > F = 0.0000 Residual | 532550149 1,714 310706.038 R-squared 0.0191 — - -- Adj R-squared = 0.0168 1,718 316010.4 Root MSE = 557.41 std. Err. t >t] [95% Conf. Interval] 79.50583 26.03277 3.05 0.002 28.44648 130.5652 nage | magesq | =-1.270711 .4357605 -2.92 0.004 -2.12539 -.4160328 prenatl0 | 69.59221 33.37728 2.09 0.037 4.127718 135.0567 prenatlOXmale | 79.16406 32.82891 2.41 0.016 14.77511 143.553 _cons | 2127.88 382.8444 5.56 0.000 1376.988 2878.772 Question: Should you conclude that the effect of prenat10 is significantly larger for male babies? ‘Why or why not? (i) Finally, consider the relationship between an infant's Apgar score at one minute (apgarlm) and the average number of cigarettes the mother smoked per day (cigs). Suppose you estimate the following regression with cigs in quadratic form: . gen cigsq = cigs"2 . reg apgarlm cigs cigsq Source | ss af MS Number of obs = 1,719 mmm Heme ee —---- F(2, 1716) = 3.99 Model | 9.8077019 2 4.90385095 Prob > F = 0.0186 Residual | 2107.61405 1,716 1.22821332 R-squared = 0.0046 + - ----- Adj R-squared = 0.0035 | 1.23249229 Root MSE = 1.1082 | Interval] [eel ieimro Ammen — cigs | -.0276565 .016572 -1.67 0.095 -.06016 .004847 | .0004735 .0007048 0.67 0.502 -.0009089 0018558 | 8.402203 .0278036 302.20 0.000 8.347671 8.456736 Question: Should you conclude that there is no significant relationship between cigarette smoking and apgarIm?

Nov 20, 2022

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