# Child's Target Height Prediction Evolution
## 4 Work Methodology Proposed
### Data Understanding  
For the proposed study, was decided to use a dataset based on the famous study 1885 of [PERSON] (an English statistician that founded concepts such as correlation, quartile, percentile and regression) that was used to analyse the relations between child's heights when adult to their parent's heights. The dataset is based on the observation of 928 children and the corresponding parents (205 pairs), where several variables have been recorded, such as father and mother height or child gender and adult height [34]. [PERSON]'s study made an important contribution in understanding multi-variable relationships and introduced the concept of regression analysis. It has proved that parents' height were two Gaussian distributions (also known as normal), one for the mother and one for the father, that, when joined together, could be described as bivariate normal. It also has proved that adult children's height could be described by a Gaussian distribution [35]. The dataset used to this experiment is composed of 898 cases and the measuring unit is the inch. The dataset file includes the following information:  
* Family: Family identification, one for each family. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Mean Squared Error** & **Accuracy** \\ \hline [PERSON] & 20.6983 & 58.55\% \\ Mid Parental & 5.2836 & 59.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Models identified on our existing literature research (our reference models) outputs. * Father: Father's height (in inches). * Mother: Mother's height (in inches)
* Sex: Child's gender: F or M.
* Height: the child's height as an adult (in inches). * Nkids: the number of adult children in the family, or, at least, the number whose heights [PERSON] recorded. Figure 2 plots the distribution of heights on mother, fathers, child's (regardless of gender), female child's and male child's. The horizontal axis represents the height, in inches, and on the vertical axis we can find the distribution density or another way the probability of a given value on the horizontal axis. Analyzing the graphic provides the following conclusions:  
* Childs gender it's a feature with high impact on height;
* All \"segments\" heights (mothers, fathers, child's, female child's and male child's) correspond to Gaussian distributions;
* Female child's and mother's height distributions are similar. The same happens with the male child's and parent's heights. The following charts allow visualizing the relation between father's heights, represented on the horizontal axis, and child's heights on the vertical axis. On the first chart (Figure 3) we used all dataset which made it possible to understand that the relation had two nuclei. This means that there are two \"focus\" on the relationship between father's and child's heights. Figure 3: Relation between father height and child height (regardless of gender). Figure 2: Heights distributions, namely mother, father, both parents, child’s, female child’s and male child’s. To understand these two different densities, we decide to split the dataset on male and female child's what can be observed in Figures 4 and 5, respectively. Figures 4 and 5 clearly identity a relation of father's height with child's height that is different when considering child's gender. For the same father height a child will be taller when male and shorter when female. The same exercise was made using the mother's height (rather than father's) and we obtain similar shapes but show different influence dimensions. This analysis outputs a high degree of influence caused by the child's gender as well as different influences from mother and father. Understanding the influence on child height were different on father and mother we have performed a correlation analysis using person correlation measure. Several approaches were implemented, such as analyzing children's height by gender or parents, according to height distribution quarters. The results can be found in Table 2.  
Figure 4: Relation between father height and male child height.