07-4-mother-daughter-bootstrap-x.Rmd

---
  title: "Art of Statistics: Figure 7.4 (page 202) Mother-Daughter regression bootstrap"
  #output: md_document
  output: html_document
---

Data as in Galton

```{r data Preparation}

library("ggplot2")
library("reshape2")

# set seed for reproducibility
set.seed(12321)
GaltonData <- read.csv("07-4-galton-x.csv") # 
GaltonMoDa <- GaltonData[GaltonData$Gender=="F",]
NumMoDa <- nrow(GaltonMoDa)

### CREATE BOOTSTRAP RESAMPLES

NumBoot <- 1000 # for interval

# Do bootstrap resampling
BootSamples <- lapply(1:NumBoot, function(n){
  SampledIndices <- sample(1:NumMoDa, NumMoDa, replace=TRUE)
  GaltonMoDa[SampledIndices,]
})

# Make a linear model for each resample
BootLMs <- lapply(BootSamples, function(X){lm(Height~Mother, data=X)})

PredNPoints <- 10
Predictable <- data.frame(Family=rep(-1, PredNPoints),
                          Father=rep(-1, PredNPoints), 
                          Mother=seq(min(GaltonData$Mother), max(GaltonData$Mother), length.out=PredNPoints), 
                          Gender=rep("F", PredNPoints),
                          Height=rep(-1, PredNPoints),
                          Kids=rep(-1,PredNPoints)
                          )

BootPredictions <- lapply(BootLMs, function(an_lm){
  data.frame(Mother=Predictable$Mother, Height=predict(an_lm, Predictable))
})

BootPredictionsDF <- melt(BootPredictions, id="Mother", value.name="Height")
BootPredictionsDF$L1 <- as.factor(BootPredictionsDF$L1)
```

Bootstrap confidence interval for gradient - see Table 9.1 on page 243
```{r}
# 95% interval on gradient?  need to extract graidents from fitted lines in plot
grads=rep(0,NumBoot)
for(i in 1:NumBoot){
  grads[i]=BootLMs[[i]]$coefficients[2]
  }
low025 =grads[order(grads)][25]
high975=grads[order(grads)][975]
mean(grads)
sd(grads)


```

###Figure 7-4 code

```{r figure 7-4 code}


p <- ggplot(GaltonMoDa, aes(x=Mother, y=Height)) # assign dataframe GaltonMoDa into plot object p

p <- p + geom_line(aes(color=L1), data=BootPredictionsDF, size=0.2) #assign dataframe BootPredictionsDF into line object and assign to plot

# alternative non-colour representation
#p <- p + scale_colour_grey(start = 0.25, end = .3)

p <- p + geom_point(shape=1, size=1, position=position_jitter(w=0.2,h=0.2)) # assign scatter chart-type to main plot data (GaltonMoDa)

p <- p + geom_smooth(method=lm, se=FALSE, size=1.5, color="black") # adds linear regression line
p <- p + scale_x_continuous(breaks = seq(58, 70, 2))
p <- p + scale_y_continuous(breaks = seq(56, 70, 2))
p <- p + theme(legend.position = "none") # removes legend
p <- p + ylab("Daughter's height") + xlab("Mother's height") # adds axis labels
p #displays plot
```

Figure 7.4 Fitted regression lines for twenty bootstrap resamples of Galton's mother-daughter height data superimposed on original data, showing the small variability in gradient due to the large sample size.