Research Question

What determines a person’s height?

• Genetics• Nutrition• Immigration / Origins• Disease

Hypothesis Brainstorming

• Sons will be similar to their Dad’s height

• Daughters will be similar to their Mom’s height

Hypotheses:

Literature Review: Article #1

• Invented Regression

• When Mid-Parents are taller then mediocrity, their Children tend to be shorter than they

• When Mid-Parents are shorter than mediocrity, their Children tend to be taller then they

Francis Galton

Literature Review: Article #2

Variables:• Genes• First two years of life• Illnesses• Infant mortality rates• Smaller Families• Higher income• Better education

Literature Review: Article #3

“we find that a 54-loci genomic profile explained 4–6% of the sex- and age-adjusted height variance”

“the Galtonian mid-parental prediction method explained 40% of the sex- and age-adjusted height variance”

Literature Review: Summary

Variable Galton Hatton AulchenkoHeight Individuals Country Average IndividualsGender Men and Women Men Only Men and WomenAge IndividualsCountries

Infant Mortality Country AverageGDP Country AverageFamily Size Country Average

Time XGenome IndividualsObservations ~1,000 550

5,478

Variables

Y

X’s

Height

Independent Variables

DependentVariable

Y

X4X3X2X1

Height Dataset Variablesheights <- read.csv("GaltonFamilies.csv")

Data Types: Numbers and Factors/Categorical

Dataset Variables: Type

Summary Statistics

Frequency Distribution, Histogram

hist(heights$childHeight)

hist(h$childHeight,freq=F, breaks =25, ylim = c(0,0.14))curve(dnorm(x, mean=mean(h$childHeight), sd=sd(h$childHeight)), col="red", add=T)

Bimodal: two modes

Mode, Bimodal

Q-Q Plot

Correlation Matrix for Continuous Variables

chart.Correlation(num2)PerformanceAnalytics package

Correlations Matrix: Both Types

library(car)scatterplotMatrix(heights)

Zoom in on Gender

Categorical: Revisit Box Plot

Note there is an equation here:Y = mx b

Correlation will depend on spread of distributions

Children Height by Gender

Linear Regression: Model 1Child’s Height = f(Father’s Height)

Linear Regression: Model 2

model.5 <- lm(childHeight~gender, data = h)

Child’s Height = f(Father’s Height)

• Mom• MidParent Height

Linear Regression: Additional Models

Compare Models

Model 1 2 12 3 4

Intercept 40.1 46.6 22.6 22.63 22.64

Father 0.385 0.36 0.01

Mom 0.314 0.29 NA

midparentHeight 0.637 0.538

Gender

R-squares 0.070 0.0395 0.105 0.102 0.1033

r 0.27 0.2 0.32

R^2 0.073 0.04 0.102

• Key Findings:• Gender was the biggest factor• Parents height played a lesser role

• Downsides• DataSet used did not include more variables of interest• DataSet for X Country for 1877

Discussion Summary

• Include More Predictor Variables• Literature review of a few articles suggests several

important factors:• Nutrition

• Analyze a Contemporary DataSet• DataSet used was from 18??• Location Specific as Well

Future Research