Predict your child's adult height

Vedrana B.

The Data Science Specialization: Developing Data Products

17.05.2015.

OVERVIEW

  • Problem description:

    • predict a child's adult height based on parent's heights

  • Problem solution:

    • linear model fit on the Galton's dataset
    • SHINY application available online

Galton's dataset (1)

  • Famous 1885 study of Francis Galton exploring the relationship between the heights of children and their parents.

  • The variables are:

    • the height of the adult child and
    • the midparent height, defined as: \[hParent = \frac{hFather + 1.08*hMother}{2}\]

  • The units are inches.

  • The number of cases is 928, representing 928 children from 205 parents.

Galton's dataset (2)

  • Data preview (interactive rCharts scatterplot):
library(UsingR); require(base64enc); require(rCharts)
data(galton)
options(RCHART_WIDTH = 600, RCHART_HEIGHT = 300)
knitr::opts_chunk$set(comment = NA, results = 'asis', tidy = F, message = T)

g1 <- nPlot(child ~ parent, data = galton, type = 'scatterChart')
g1$show('inline', include_assets = TRUE)

Prediction model (1)

  • Linear model = linear relationship between input variable (parent height) and the output (child height)

    \[hChild = \alpha * hParent + \beta\]

  • where to build the model:

    • \(hParent\) and \(hChild\) are taken from the datasets
    • \(\alpha\) and \(\beta\) are model parameters calculated so that the data fits the equation with the minimal sum of squared residuals

Prediction model (2)

  • chunk of R code for building the model and for predicting:
model <- lm(formula = child ~ parent, data = galton2)
p     <- (as.numeric(input$hF) + 1.08*as.numeric(input$hM))/2
c     <- predict(model, data.frame(parent = p))

Prediction model (3)

  • Plot of the linear model fit to the Galton data in inches:
library(ggplot2)
limits <- c(min(galton)-1,max(galton)+1)
ggplot(data = galton, aes(x=parent,y=child))             + 
    geom_point(color = "red", alpha=0.2, size=3)         +
    labs(x = "Parent\'s height", y = "Child\'s height")  +
    labs(title ="LM prediction using Galton\'s dataset") + 
    coord_cartesian(xlim = limits, ylim = limits)        +
    geom_smooth(method='lm')                             +
    guides(color = FALSE, fill = FALSE)

plot of chunk plot2

Interactive SHINY web app

  • Screenshot:

REFERENCES:

Thank you!