<p>Quantile regression have its advantage properties comparing to the OLS model regression which are full measurement of the effects of a covariate on response, robustness and Equivariance property. In this paper, I use a survey data in Belgium and apply a linear model to see the advantage properites of quantile regression. And I use a quantile regression model with the raw data to analyze the different cost of family on different numbers of children and apply a Wald test. The result shows that for most of the family types and living standard, from the lower quantile to the upper quantile the family cost on children increases along with the increasing number of children and the cost of each child is the same. And we found a common behavior that the cost of the second child is significantly more than the cost of the first child for a nonworking type of family and all living standard families, at the upper quantile (from 0.75 quantile to 0.9 quantile) of the conditional distribution.</p>

Quantile regression have its advantage properties comparing to the OLS model regression which are full measurement of the effects of a covariate on response, robustness and Equivariance property. In this paper, I use a survey data in Belgium and apply a linear model to see the advantage properites of quantile regression. And I use a quantile regression model with the raw data to analyze the different cost of family on different numbers of children and apply a Wald test. The result shows that for most of the family types and living standard, from the lower quantile to the upper quantile the family cost on children increases along with the increasing number of children and the cost of each child is the same. And we found a common behavior that the cost of the second child is significantly more than the cost of the first child for a nonworking type of family and all living standard families, at the upper quantile (from 0.75 quantile to 0.9 quantile) of the conditional distribution.