Observe that the Poisson intercept in this CEB Distribution and Poisson Distribution with mu=1.855 model, which has no independent variables, is. 6178104. We exponentiate this value that is. e 6178104= 1.854862 which is indeed the mean of the CEB Now we use the "prcounts"command to graph the observed distribution of the CEB variable with a univariate poisson distribution with a mean of 1 855 Observed CEB Distrbution -+Unvariate Poisson, mu=13 Stata command The graph shows that the children ever bon ariable is pretty much Poisson distributed The univariate poisson distribution over- prcounts cebprob, plot max(10) predicts the observed CeB distribution at the label var cebprobobeq "Observed CEB Distribution count of zero, and under-predicts counts of 1 label var cebprobpreg Univariate Poisson, mu= and 2; the remaining counts are pretty close 855 label var cebprobval " Number of Children Ever Borm The observed CEB distribution, compared to the univariate poisson distribution with a graph twoway connected cebprobobeq cebprobpreq mean, u,of 1.855, has substantially fewer cebprobval, title("Proportion or Probability) 0s, and more cases in the earlier counts label(0(1). 4) xlabel(o(1)9)title("CEB Distribution and Poisson Distribution with mu=1.855) Even though the two distributions are not perfect, we may conclude that we are correct in estimating the CEB dependent variable with a poisson model13 25 • Observe that the Poisson intercept in this model, which has no independent variables, is .6178104 . We exponentiate this value, that is, e.6178104 = 1.854862, which is indeed the mean of the “CEB” variable. • Now we use the “prcounts” command to graph the observed distribution of the CEB variable with a univariate Poisson distribution with a mean of 1.855. 26 Stata command: prcounts cebprob, plot max(10) label var cebprobobeq "Observed CEB Distribution" label var cebprobpreq "Univariate Poisson, mu = 1.855" label var cebprobval "Number of Children Ever Born" graph twoway connected cebprobobeq cebprobpreq cebprobval, ytitle("Proportion or Probability") ylabel(0(.1).4) xlabel(0(1) 9) title("CEB Distribution and Poisson Distribution with mu = 1.855") 14 27 0 .1 .2 .3 .4 Proportion or Probability 0 1 2 3 4 5 6 7 8 9 Number of Children Ever Born Observed CEB Distribution Univariate Poisson, mu = 1.855 CEB Distribution and Poisson Distribution with mu = 1.855 28 • The graph shows that the children ever born variable is pretty much Poisson distributed. The univariate Poisson distribution over￾predicts the observed CEB distribution at the count of zero, and under-predicts counts of 1 and 2; the remaining counts are pretty close. The observed CEB distribution, compared to the univariate Poisson distribution with a mean, μ, of 1.855, has substantially fewer 0’s, and more cases in the earlier counts. Even though the two distributions are not perfect, we may conclude that we are correct in estimating the CEB dependent variable with a Poisson model