regression

Regression Examples

install.packages("UsingR",repos = "http://cran.us.r-project.org")

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library(UsingR)

## Loading required package: MASS

## Loading required package: HistData

## Loading required package: Hmisc

## Loading required package: lattice

## Loading required package: survival

## Loading required package: Formula

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 3.3.2

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## Attaching package: 'Hmisc'

## The following objects are masked from 'package:base':
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## Attaching package: 'UsingR'

## The following object is masked from 'package:survival':
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data(galton)
head(galton)

##   child parent
## 1  61.7   70.5
## 2  61.7   68.5
## 3  61.7   65.5
## 4  61.7   64.5
## 5  61.7   64.0
## 6  62.2   67.5

par(mfrow=c(1,2))
hist(galton$child, col="blue", breaks=100)
abline(h = mean(galton$child), v = mean(galton$child), col="red", lwd=1, lty=1)
hist(galton$parent, col="red", breaks=100)
abline(h = mean(galton$parent), v = mean(galton$parent), col="blue", lwd=1, lty=1)

The least squares estimate is the empirical mean

hist(galton$child, col="blue", breaks = 100)
meanChild<-mean(galton$child)
lines(rep(meanChild, 100), seq(0, 150, length=100), col="red", lwd=5)

Comparing Childrens Height and their Parents heights

plot(galton$parent, galton$child, pch=19, col="blue")

Complete linear regression

install.packages("dplyr",repos = "http://cran.us.r-project.org")

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library(dplyr)

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## Attaching package: 'dplyr'

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## The following object is masked from 'package:MASS':
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## The following objects are masked from 'package:stats':
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## The following objects are masked from 'package:base':
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freqData <- as.data.frame(table(galton$child, galton$parent))
names(freqData) <- c("child", "parent", "freq")
freqData$child <- as.numeric(as.character(freqData$child))
freqData$parent <- as.numeric(as.character(freqData$parent))
g <- ggplot(filter(freqData, freq > 0), aes(x = parent, y = child))
g <- g  + scale_size(range = c(2, 10), guide = "none" )
g <- g + geom_point(colour="blue", aes(size = freq+10, show_guide = FALSE))

## Warning: Ignoring unknown aesthetics: show_guide

g <- g + geom_point(aes(colour=freq, size = freq))
g <- g + scale_colour_gradient(low = "white", high="red")                    
lm1 <- lm(galton$child ~ galton$parent)
g <- g + geom_abline(intercept = coef(lm1)[1], slope = coef(lm1)[2], size = 1, colour = grey(.5))
g