Do Age, Place of Birth and Age at First Birth Predict Number of Children Born to an Individual - Statistics Project Example

Regression Analysis of General Social Survey Data: Do Age, Place of Birth and Age at First Birth Predict Number of Children Born to an Individual? Group Members: Institutional Affiliation Introduction Source of the Data This research investigates the relationship between age, age at first birth, place of birth, and number of children born to a group of respondents in the General Social Survey (GSS) of 2012 (the latest year for which data has been recorded). The GSS runs social surveys once a year. The SPSS version of the data was downloaded from the General Social Survey’s website (http://www3.norc.org/GSS+Website/). Data used in this analysis corresponds to 55 of the first 70 respondents in the survey. Data below this point was truncated for the purpose of using a smaller but adequate sample for this analysis. The 15 respondents from within the first 70 whose information was removed did not meet the criterion set out – each respondent included in the analysis must have had child(ren) at the time of the survey. Description of the Variables The research seeks to establish whether 1) the age of the respondent at the time of the survey is a determinant of the number of children they have; 2) the age at which a respondent in the survey gave birth to their first child is a predictor of the number of children they had at the time of the survey; and 3) whether there is a relationship between the place of birth of the respondent and their numbers of children. Therefore, the number of children born to the respondent is the dependent variable throughout the analysis. The age of the respondent is a continuous variable estimated up to the time the survey was carried out. Equally, the “age at first birth” is a continuous variable denoting the age at which the first child (alive or dead) was born to the respondent. The “place of birth” is a binary categorical variable and denotes the country in which the respective respondent was born. They are classified as either “born in the US, denoted by the digit 1”, or “born outside the US, denoted by the digit 2”. The data used in included in the appendix. X1 = Age of respondent at the time of the survey. X2 = Age at which the respondent had their first child born to them. X3 = Respondents’ places of birth. Y = Number of children born to the respondent at the time of the survey. Analysis All tests have been carried out at the 5% level of significance. The first regression model seeks to establish whether the ages of respondents are predictors of the number of children they have. According to the output, age is not a significant predictor of the number of children that respondents have (F = 3.713, p = 0.059). The regression model for this relationship is: Number of Children = 1.39 + 0.025*Age. The Excel output obtained is given below. Regression Statistics Multiple R 0.255873806 R Square 0.065471404 Adjusted R Square 0.047838789 Standard Error 1.474755205 Observations 55 ANOVA   df SS MS F Significance F Regression 1 8.075600134 8.075600134 3.713085345 0.059356024 Residual 53 115.2698544 2.174902913 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.390144072 0.712779444 1.950314482 0.05643604 -0.03951041 2.819798555 -0.03951041 2.819798555 Age of Respondent 0.025444432 0.013204601 1.926936778 0.059356024 -0.001040644 0.051929508 -0.001040644 0.051929508 The second model investigates whether the age at which a respondent gave birth is a predictor of the number of children they have. The output indicates that the dependent variable is a significant predictor of the dependent variable (F = 14.67, p = 0.0003). The following regression model is obtained. Number of Children = 5.637 – 0.1118*Age at First Birth. The Excel output is displayed below. Regression Statistics Multiple R 0.465563766 R Square 0.21674962 Adjusted R Square 0.201971311 Standard Error 1.350124901 Observations 55 ANOVA   df SS MS F Significance F Regression 1 26.7350804 26.7350804 14.66674023 0.000341294 Residual 53 96.61037415 1.822837248 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.636734694 0.785832437 7.172947348 2.37587E-09 4.060554467 7.21291492 4.060554467 7.21291492 Respondents Age at First Birth -0.111819728 0.029197901 -3.829718035 0.000341294 -0.170383299 -0.053256156 -0.170383299 -0.053256156 The third model seeks to establish whether being born in or outside the US is predictive of the number of children a respondent in the GSS has. From the output, this variable is not a significant predictor of the dependent variable (F = 1.417, p = 0.239). The regression equation corresponding to the test is: Number of Children = 2.026 + 0.515*Place of Birth. Below are the results of this test. Regression Statistics Multiple R 0.161366762 R Square 0.026039232 Adjusted R Square 0.007662614 Standard Error 1.505547187 Observations 55 ANOVA   df SS MS F Significance F Regression 1 3.211820912 3.211820912 1.416976272 0.239206321 Residual 53 120.1336336 2.266672333 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.025525526 0.609074625 3.325578581 0.001606968 0.803876565 3.247174486 0.803876565 3.247174486 Place of Birth(1 = US, 2 = Elsewhere) 0.515015015 0.432651887 1.190368125 0.239206321 -0.352774754 1.382804784 -0.352774754 1.382804784 The fourth model combines the first two independent variables, age and age at first birth, assessing whether they are significant predictors of the number of children by an individual in the survey. The results indicate that individual’s age and age at which the individual had their first birth are joint significant predictors of the number of children by a respondent (F = 9.506, p = 0.0003). The regression model for this relationship is: Number of Children = 4.377 + 0.022*Age of Respondent – 0.108*Age at First Birth. The output is displayed below. Regression Statistics Multiple R 0.517417616 R Square 0.26772099 Adjusted R Square 0.239556412 Standard Error 1.317947759 Observations 55 ANOVA   df SS MS F Significance F Regression 2 33.02216717 16.51108358 9.505592315 0.000303104 Residual 52 90.32328738 1.736986296 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4.376955291 1.01336787 4.319216564 7.06552E-05 2.343483937 6.410426646 2.343483937 6.4104266 Age of Respondent 0.022499341 0.011826147 1.902508173 0.062649103 -0.001231558 0.046230239 -0.001231558 0.0462302 Respondents Age at First Birth -0.10824872 0.028563774 -3.78972066 0.000393476 -0.165566127 -0.050931319 -0.165566127 -0.0509313 The fifth model replaces the variable “age” with the “country of birth” of the respondent, such that the new predictors of the number of children become respondent’s age at the time of the survey, and country of birth. From the results, the age of a respondent and the country of birth are joint significant predictors of the number of children born to the individual (F = 3.585, p = 0.035). The regression equation is shown below. Number of Children = 0.0271 + 0.0318*Age of Respondent + 0.7801*Place of Birth. Below is the Excel output. Regression Statistics Multiple R 0.348102641 R Square 0.121175449 Adjusted R Square 0.087374504 Standard Error 1.443813152 Observations 55 ANOVA   df SS MS F Significance F Regression 2 14.94644079 7.473220397 3.584972291 0.034790183 Residual 52 108.3990138 2.084596418 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.027132704 1.024993206 0.026471106 0.978982908 -2.029666593 2.083932001 -2.029666593 2.083932001 Age of Respondent 0.03176443 0.013388057 2.372594501 0.021397104 0.004899329 0.058629531 0.004899329 0.058629531 Place of Birth(1 = US, 2 = Elsewhere) 0.780100154 0.429691159 1.81549035 0.075216794 -0.08213822 1.642338527 -0.08213822 1.642338527 The sixth regression analysis investigates whether the number of children can be successfully, simultaneously predicted from the age at which a respondent had their first child and their country of birth. Both variables are joint significant predictors of the number of children born to the respondent at the time of the interviews (F = 7.983, p = 0.0009). The accompanying regression equation is: Number of Children = 5.016 – 0.1100*Respondent’s Age at First Birth + 0.4308*Country of Birth. Below is the corresponding regression output. Regression Statistics Multiple R 0.484675429 R Square 0.234910272 Adjusted R Square 0.205483744 Standard Error 1.347150414 Observations 55 ANOVA   df SS MS F Significance F Regression 2 28.97511424 14.48755712 7.98294218 0.000947374 Residual 52 94.37034031 1.814814237 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.016005073 0.962797185 5.209825239 3.2917E-06 3.084011221 6.947998925 3.084011221 6.947998925 Respondents Age at First Birth -0.109951384 0.02918207 -3.767771878 0.00042159 -0.16850949 -0.051393277 -0.16850949 -0.051393277 Place of Birth(1 = US, 2 = Elsewhere) 0.430818009 0.387777537 1.110992689 0.27168223 -0.34731453 1.208950548 -0.34731453 1.208950548 The seventh model seeks to establish whether the three dependent variables; age of the respondent, age at first birth, and country of birth are joint significant predictors of the number of children born to a respondent in the survey. From the results, the three independent variables are indeed joint significant predictors of the number of children (F = 7.582, p = 0.0003). The regression equation depicting this relationship is: Number of Children = 3.104 + 0.028*Age of Respondent – 0.1045*Age at First Birth + 0.6689*Country of Birth. The output for the analysis is shown below. Regression Statistics Multiple R 0.55536002 R Square 0.30842475 Adjusted R Square 0.26774386 Standard Error 1.29329086 Observations 55 ANOVA   df SS MS F Significance F Regression 3 38.0427913 12.68093043 7.581562256 0.000275333 Residual 51 85.30266325 1.67260124 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3.10409335 1.236367858 2.510655168 0.015263218 0.621981358 5.586205346 0.621981358 5.586205346 Age of Respondent 0.02802087 0.012034547 2.328369035 0.023894918 0.003860506 0.052181229 0.003860506 0.052181229 Respondents Age at First Birth -0.1044717 0.028114038 -3.715998017 0.000503285 -0.160912993 -0.048030424 -0.160912993 -0.048030424 Place of Birth(1 = US, 2 = Elsewhere) 0.66885798 0.38605685 1.732537515 0.089221998 -0.106183475 1.443899425 -0.106183475 1.443899425 Besides age and age at first birth, the eighth model incorporates an interaction term of the ages of respondents and ages at first birth to investigate whether the interaction term affects the outcome of number of children born to the GSS respondents. Again, the predictor variables significantly predict the outcome (F = 6.61, p = 0.0007). This predictive relationship is demonstrated by the equation: Number of Children = 2.017 + 0.0696*Age of Respondent – 0.0083*Age at First Birth – 0.002*(Age*Age at First Birth). Below is the output. Regression Statistics Multiple R 0.529117977 R Square 0.279965834 Adjusted R Square 0.237610883 Standard Error 1.31963261 Observations 55 ANOVA   df SS MS F Significance F Regression 3 34.53251305 11.51083768 6.60999075 0.000737616 Residual 51 88.8129415 1.741430225 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.017207234 2.729455025 0.739051281 0.46326386 -3.462402261 7.496816729 -3.462402261 7.496816729 Age of Respondent 0.069580398 0.051922898 1.340071529 0.186162224 -0.034659168 0.173819964 -0.034659168 0.173819964 Respondents Age at First Birth -0.008296848 0.111071558 -0.07469822 0.940747054 -0.2312823 0.214688604 -0.2312823 0.214688604 X1X2 (Age*Birth Age) -0.001996806 0.002144128 -0.93129049 0.356091061 -0.006301322 0.00230771 -0.006301322 0.00230771 The ninth test sought to establish age and its square are significant predictors of number of children, in a non-linear formation. The non-linear equation so formed cannot significantly predict the outcome (F = 2.681, p = 0.078). The relationship is shown as: Number of Children = 4.284 – 0.0899*Age of Respondent + 0.0011*(Age)2. The output is shown below. Regression Statistics Multiple R 0.305751961 R Square 0.093484262 Adjusted R Square 0.058618272 Standard Error 1.466383541 Observations 55 ANOVA   df SS MS F Significance F Regression 2 11.53085874 5.765429369 2.681245011 0.077939759 Residual 52 111.8145958 2.150280689 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4.283561251 2.390039883 1.792255134 0.078910646 -0.512404538 9.079527041 -0.51240454 9.079527041 Age of Respondent -0.08989345 0.091929424 -0.977852867 0.332674604 -0.274363331 0.09457643 -0.27436333 0.09457643 X1(Squared) 0.001058851 0.000835299 1.267630562 0.210577007 -0.0006173 0.002735001 -0.0006173 0.002735001 The final test investigates whether age of a respondent at the time of first birth, and its square, are significant predictors of the number of children they have. The non-linear relationship is statistically significant (F = 8.279, p = 0.0008). The equation of the relationship is: Number of Children = 9.481 – 0.4114*Age at First Birth + 0.0055*(Age at First Birth)2. Below is the respective output for the relationship. Regression Statistics Multiple R 0.491443261 R Square 0.241516479 Adjusted R Square 0.212344036 Standard Error 1.341321784 Observations 55 ANOVA   df SS MS F Significance F Regression 2 29.78995991 14.89497996 8.278925366 0.000756136 Residual 52 93.55549463 1.799144128 Total 54 123.3454545         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 9.480791769 3.051582556 3.106844267 0.003061393 3.357343518 15.60424002 3.357343518 15.60424002 Respondents Age at First Birth -0.411430175 0.231751098 -1.775310576 0.081699171 -0.876472764 0.053612415 -0.87647276 0.053612415 X2(Squared) 0.005522488 0.004238095 1.303058955 0.198295342 -0.002981872 0.014026847 -0.00298187 0.014026847 Finally, I choose on the model which incorporates the three predictor variables as the one depicting the “best fit” from the others. This is done on the basis of the strength of the p-value (0.00027), which is smaller than the p-values in the other 9 models. Testing for normality, the normal probability plot is bow-shaped, indicating non-normality. The plot of residuals indicates values that grow along the x-axis, which is proof for violation of homoscedasticity. Few residuals fall outside the ±2 range, which indicates violation of the assumption of independence. On a plot of the expected versus actual number of children, the values do not appear to follow a linear pattern along the line of “best fit”. Therefore, the data violates the assumption of linearity as well. Essentially, the model violates all four selected assumptions of regression. The selected model has the form: Number of Children = 3.104 + 0.028*Age of Respondent – 0.1045*Age at First Birth + 0.6689*Country of Birth. The first slope indicates that when one more child is born to a respondent in the survey, the respondent’s age is likely to have grown by 0.028 years; their age at first birth is likely to be 0.1045 lesser years, and they are 0.6689 times more likely to have been born outside the US. For instance, if we assumed a 26-year-old gave birth to their first born at age 20, and was born within the US, we can estimate the number of children they have as: Number of Children = 3.104 + 0.028*26 – 0.1045*20 + 0.6689*(1) = 2.41, approximately 2 children. References General Social Survey (2012). Download data: Social survey data - 2012. Retrieved from http://www3.norc.org/GSS+Website/Download/SPSS+Format/ (Accessed 30th September, 2014). Appendix Data Age of Respondent Respondents Age at First Birth Place of Birth(1 = US, 2 = Elsewhere) Number of Children X1X2 (Age*Birth Age) X1(Squared) X2(Squared) 42 32 1 2 1344 1764 1024 49 24 1 2 1176 2401 576 70 24 1 3 1680 4900 576 50 25 1 2 1250 2500 625 35 23 1 2 805 1225 529 24 17 2 3 408 576 289 28 18 1 2 504 784 324 55 22 1 6 1210 3025 484 36 26 1 3 936 1296 676 28 20 1 4 560 784 400 59 16 1 6 944 3481 256 52 18 2 4 936 2704 324 35 25 1 4 875 1225 625 36 28 2 3 1008 1296 784 47 21 1 5 987 2209 441 55 34 2 6 1870 3025 1156 76 18 2 8 1368 5776 324 39 25 2 1 975 1521 625 54 23 1 2 1242 2916 529 45 28 2 2 1260 2025 784 71 37 1 2 2627 5041 1369 42 27 2 2 1134 1764 729 50 33 1 2 1650 2500 1089 81 27 1 3 2187 6561 729 44 22 1 2 968 1936 484 63 28 1 2 1764 3969 784 40 34 2 1 1360 1600 1156 62 33 1 2 2046 3844 1089 30 17 1 2 510 900 289 69 27 1 2 1863 4761 729 57 27 1 3 1539 3249 729 44 34 1 2 1496 1936 1156 73 22 1 3 1606 5329 484 73 22 1 3 1606 5329 484 68 35 1 2 2380 4624 1225 84 23 1 4 1932 7056 529 63 26 1 1 1638 3969 676 57 29 1 2 1653 3249 841 42 29 2 2 1218 1764 841 45 37 2 2 1665 2025 1369 38 33 1 1 1254 1444 1089 46 33 1 2 1518 2116 1089 51 30 2 3 1530 2601 900 41 23 2 1 943 1681 529 75 21 1 3 1575 5625 441 81 18 2 5 1458 6561 324 41 18 2 6 738 1681 324 67 19 1 2 1273 4489 361 71 23 1 2 1633 5041 529 35 28 2 2 980 1225 784 45 42 1 1 1890 2025 1764 35 33 2 2 1155 1225 1089 52 17 2 2 884 2704 289 49 36 1 1 1764 2401 1296 51 30 1 2 1530 2601 900 Read More