1. What factors are most responsible for height?
Outcome = (Model) Error

2. Analytics & History: 1st Regression Line
The first “Regression Line”

3. Galton’s Notebook on Families & Height

4. Galton’s Family Height DatasetX1 X2 X3 Y

5. > getwd()
[1] "C:/Users/johnp_000/Documents"
> setwd()

6. Dataset Input h <- read.csv("GaltonFamilies.csv") Object Function
Filename
Data()

7. str() summary()
Data Types: Numbers and Factors/Categorical

8. Outline One Variable: Univariate Two Variables: Bivariate
Dependent / Outcome Variable
Two Variables: Bivariate
Outcome and each Predictor
All Four Variables: Multivariate

9. Variable Type Steps Y X1, X2 X3 Histogram Child’s Height Continuous
Dad’s Height
X1, X2
Scatter
Continuous
Mom’s Height X3
Gender
Categorical
Boxplot
Linear
Regression

10. Frequency Distribution, Histogram
hist(h$child)
Frequency Distributions: A graph plotting values of observations on the horizontal axis, with a bar showing how many times each value occurred in the data set.

11. Density Plot
plot(density(h$childHeight))
Area = 1

12. Mode, Bimodal 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)

13. Asst. Professor of Statistics at Rice University
Industries / Organizations Creating and Using R
Hadley Wickham
Asst. Professor of Statistics at Rice University
Industry
Pct.
Research
24%
Higher Education 7%
Information Technology 9%
Computer Software
Financial Services 6%
Banking 2%
Pharmaceuticals 4%
Biotechnology
Market Research 3%
Management Consulting
Total
69%
ggplot2
plyr
reshape
rggobi
profr
Source: LinkedIN R Group (Sept, 2011)

14. ggplot2 library(ggplot2) h.gg <- ggplot(h, aes(child))
h.gg + geom_histogram(binwidth = 1 ) + labs(x = "Height", y = "Frequency")
h.gg + geom_density()

15. ggplot2
h.gg <- ggplot(h, aes(child)) + theme(legend.position = "right")
h.gg + geom_density() + labs(x = "Height", y = "Frequency")
h.gg + geom_density(aes(fill=factor(gender)), size=2)

16. Variable Type Steps Y X1, X2 X3 Histogram Child’s Height Continuous
Dad’s Height
X1, X2
Scatter
Continuous
Mom’s Height X3
Gender
Categorical
Boxplot
Linear
Regression

17. Correlation and Regression

19. Covariance
Calculate the difference between the mean and each person’s score for the first variable (x).
Calculate the difference between the mean and their value for the second variable (y).
Multiply these “error” values.
Add these values to get the cross product deviations.
The covariance is the average of cross-product deviations

20. Covariance Y X
Persons 2,3, and 5 look to have similar magnitudes from their means

21. Covariance
Calculate the error [deviation] between the mean and each subject’s score for the first variable (x).
Calculate the error [deviation] between the mean and their score for the second variable (y).
Multiply these error values.
Add these values and you get the cross product deviations.
The covariance is the average cross-product deviations:

22. Standardizing the Covariance
Covariance depends upon the units of measurement
Normalize the data
Divide by the standard deviations of both variables.
The standardized version of covariance is known as the correlation coefficient

23. Correlation
?cor
cor(h$father, h$child)

24. Scatterplot Matrix: pairs()

25. Correlations Matrix
library(car) scatterplotMatrix(heights)

26. ggplot2

27. Variable Type Steps Y X1, X2 X3 Histogram Child’s Height Continuous
Dad’s Height
X1, X2
Scatter
Continuous
Mom’s Height X3
Gender
Categorical
Boxplot
Linear
Regression

28. Box Plot

29. Children’s Height vs. Gender
boxplot(h$child~gender,data=h, col=(c("pink","lightblue")),
main="Children's Height by Gender", xlab="Gender", ylab="")

30. Descriptive Stats: Box Plot
69.23
64.10
======
5.13

31. Subset Males
men<- subset(h, gender=='male')

32. Subset Females
women <- subset(h, gender==‘female')

33. Children’s Height: Males
hist(men$childHeight)
qqnorm(men$childHeight)
qqline(men$childHeight)

34. Children’s Height: Females
hist(women$child)
qqnorm(women$child)
qqline(women$child)

35. ggplot2 library(ggplot2)
h.bb <- ggplot(h, aes(factor(gender), child))
h.bb + geom_boxplot()
h.bb + geom_boxplot(aes(fill = factor(gender)))