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Introduction to R for Data Science
Lecturers
dipl. ing Branko Kovač
Data Analyst at CUBE/Data Science Mentor
at Springboard
Data Science zajednica Srbije
branko.kovac@gmail.com
dr Goran S. Milovanović
Data Scientist at DiploFoundation
Data Science zajednica Srbije
goran.s.milovanovic@gmail.com
goranm@diplomacy.edu
Linear Regression in R
• Exploratory Data Analysis
• Assumptions of the Linear Model
• Correlation
• Normality Tests
• Linear Regression
• Prediction, Confidence
Intervals, Residuals
• Influential Cases and
the Influence Plot
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# clear
rm(list=ls())
#### read data
library(datasets)
data(iris)
### iris data set description:
# https://stat.ethz.ch/R-manual/R-devel/library/iriss/html/iris.html
### ExploratoryData Analysis (EDA)
str(iris)
summary(iris)
Linear Regression in R
• Before modeling: Assumptions and Exploratory Data Analysis (EDA)
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
### EDA plots
# plot layout:2 x 2
par(mfcol = c(2,2))
# boxplotiris$Sepal.Length
boxplot(iris$Sepal.Length,
horizontal = TRUE,
xlab="Sepal Length")
# histogram:iris$Sepal.Length
hist(iris$Sepal.Length,
main="",
xlab="Sepal.Length",
prob=T)
# overlay iris$Sepal.Length density functionoverthe empiricaldistribution
lines(density(iris$Sepal.Length),
lty="dashed",
lwd=2.5,
col="red")
EDA
Intro to R for Data Science
Session 6: Linear Regression in R
Linear Regression in R
• EDA
Intro to R for Data Science
Session 6: Linear Regression in R
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
## Pearsoncorrelationin R {base}
cor1 <- cor(iris$Sepal.Length, iris$Petal.Length,
method="pearson")
cor1
par(mfcol = c(1,1))
plot(iris$Sepal.Length, iris$Petal.Length,
main = "Sepal Length vs Petal Length",
xlab = "Sepal Length", ylab = "Petal Length")
## Correlation matrix and treatmentof missing data
dSet <- iris
# Remove one discretevariable
dSet$Species <- NULL
# introduce NA in dSet$Sepal.Length[5]
dSet$Sepal.Length[5] <- NA
# Pairwise and Listwise Deletion:
cor1a <- cor(dSet,use="complete.obs") # listwise deletion
cor1a <- cor(dSet,use="pairwise.complete.obs") # pairwise deletion
cor1a <- cor(dSet,use="all.obs") # all observations -error
Correlation
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
library(Hmisc)
cor2 <- rcorr(iris$Sepal.Length,
iris$Petal.Length,
type="pearson")
cor2$r # correlations
cor2$r[1,2] # that's whatyou need,right
cor2$P # significantat
cor2$n # num.observations
# NOTE: rcorr uses Pairwise deletion!
# Correlation matrix
cor2a <- rcorr(as.matrix(dSet),
type="pearson") # NOTE:as.matrix
# select significant at alpha == .05
w <- which(!(cor2a$P<.05),arr.ind = T)
cor2a$r[w] <- NA
cor2a$P # comparew.
cor2a$r
Correlation {Hmisc}
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# LinearRegression:lm()
# Predicting:PetalLength from SepalLength
reg <- lm(Petal.Length ~ Sepal.Length, data=iris)
class(reg)
summary(reg)
coefsReg <- coefficients(reg)
coefsReg
slopeReg <- coefsReg[2]
interceptReg <- coefsReg[1]
# Prediction from this model
newSLength <- data.frame(Sepal.Length = runif(100,
min(iris$Sepal.Length),
max(iris$Sepal.Length))
) # watch the variable namesin the new data.frame!
predictPLength <- predict(reg, newSLength)
predictPLength
Linear Regression with lm()
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# Standardizedregressioncoefficients {QuantPsych}
library(QuantPsyc)
lm.beta(reg)
# Reminder:standardizedregressioncoefficientsare...
# What you would obtain upon performinglinearregressionoverstandardizedvariables
# z-score in R
zSLength <- scale(iris$Sepal.Length, center = T, scale = T) # computes z-score
zPLength <- scale(iris$Petal.Length, center = T, scale = T) # again;?scale
# new dSetw. standardized variables
dSet <- data.frame(Sepal.Length <- zSLength,
Petal.Length <- zPLength)
# LinearRegression w.lm() overstandardized variables
reg1 <- lm(Petal.Length ~ Sepal.Length, data=dSet)
summary(reg1)
# compare
coefficients(reg1)[2] # beta from reg1
lm.beta(reg) # standardizedbeta w. QuantPscy lm.beta from reg
Standardized Regression Coefficients
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# plots w. {base}and {ggplot2}
library(ggplot2)
# Predictorvs Criterion {base}
plot(iris$Sepal.Length, iris$Petal.Length,
main = "Petal Length vs Sepal Length",
xlab = "Sepal Length",
ylab = "Petal Length"
)
abline(reg,col="red")
# Predictorvs Criterion {ggplot2}
ggplot(data = iris,
aes(x = Sepal.Length, y = Petal.Length)) +
geom_point(size = 2, colour = "black") +
geom_point(size = 1, colour = "white") +
geom_smooth(aes(colour = "red"),
method='lm') +
ggtitle("Sepal Length vs Petal Length") +
xlab("Sepal Length") + ylab("Petal Length") +
theme(legend.position = "none")
Plots {base} vs {ggplot2}
Intro to R for Data Science
Session 6: Linear Regression in R
Plots {base} vs {ggplot2}
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# Predicted vs.residuals {ggplot2}
predReg <- predict(reg) # get predictions from reg
resReg <- residuals(reg) # get residuals from reg
# resStReg <- rstandard(reg)# get residualsfrom reg
plotFrame <- data.frame(predicted = predReg,
residual = resReg);
ggplot(data = plotFrame,
aes(x = predicted, y = residual)) +
geom_point(size = 2, colour = "black") +
geom_point(size = 1, colour = "white") +
geom_smooth(aes(colour = "blue"),
method='lm',
se=F) +
ggtitle("Predicted vs Residual Lengths") +
xlab("Predicted Lengths") + ylab("Residual") +
theme(legend.position = "none")
Predicted vs Residuals
Intro to R for Data Science
Session 6: Linear Regression in R
Predicted vs Residuals
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
## Detectinfluentialcases
infReg <- as.data.frame(influence.measures(reg)$infmat)
# Cook's Distance:Cook and Weisberg(1982):
# values greaterthan 1 are troublesome
wCook <- which(infReg$cook.d>1) # we're fine here
# Average Leverage = (k+1)/n,k - num. of predictors,n - num. observations
# Also termed:hat values,range:0 - 1
# see: https://en.wikipedia.org/wiki/Leverage_%28statistics%29
# Various criteria (twice the leverage,three times the average...)
wLev <- which(infReg$hat>2*(2/length(iris$price))) # we seem to be fine here too...
## Influenceplot
infReg <- as.data.frame(influence.measures(reg)$infmat)
plotFrame <- data.frame(residual = resStReg,
leverage = infReg$hat,
cookD = infReg$cook.d)
Infulential Cases + Infulence Plot
Intro to R for Data Science
Session 6: Linear Regression in R
# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
ggplot(plotFrame,
aes(y = residual,
x = leverage)) +
geom_point(size = plotFrame$cookD*100, shape = 1) +
ggtitle("Influence PlotnSize of the circle corresponds to Cook's distance") +
theme(plot.title = element_text(size=8, face="bold")) +
ylab("Standardized Residual") + xlab("Leverage")
Infulence Plot
Intro to R for Data Science
Session 6: Linear Regression in R
Infulence Plot
Intro to R for Data Science
Session 6: Linear Regression in R
Introduction to R for Data Science :: Session 6 [Linear Regression in R]

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Introduction to R for Data Science :: Session 6 [Linear Regression in R]

  • 1. Introduction to R for Data Science Lecturers dipl. ing Branko Kovač Data Analyst at CUBE/Data Science Mentor at Springboard Data Science zajednica Srbije branko.kovac@gmail.com dr Goran S. Milovanović Data Scientist at DiploFoundation Data Science zajednica Srbije goran.s.milovanovic@gmail.com goranm@diplomacy.edu
  • 2. Linear Regression in R • Exploratory Data Analysis • Assumptions of the Linear Model • Correlation • Normality Tests • Linear Regression • Prediction, Confidence Intervals, Residuals • Influential Cases and the Influence Plot Intro to R for Data Science Session 6: Linear Regression in R
  • 3. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 # clear rm(list=ls()) #### read data library(datasets) data(iris) ### iris data set description: # https://stat.ethz.ch/R-manual/R-devel/library/iriss/html/iris.html ### ExploratoryData Analysis (EDA) str(iris) summary(iris) Linear Regression in R • Before modeling: Assumptions and Exploratory Data Analysis (EDA) Intro to R for Data Science Session 6: Linear Regression in R
  • 4. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 ### EDA plots # plot layout:2 x 2 par(mfcol = c(2,2)) # boxplotiris$Sepal.Length boxplot(iris$Sepal.Length, horizontal = TRUE, xlab="Sepal Length") # histogram:iris$Sepal.Length hist(iris$Sepal.Length, main="", xlab="Sepal.Length", prob=T) # overlay iris$Sepal.Length density functionoverthe empiricaldistribution lines(density(iris$Sepal.Length), lty="dashed", lwd=2.5, col="red") EDA Intro to R for Data Science Session 6: Linear Regression in R
  • 5. Linear Regression in R • EDA Intro to R for Data Science Session 6: Linear Regression in R
  • 6. Intro to R for Data Science Session 6: Linear Regression in R
  • 7. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 ## Pearsoncorrelationin R {base} cor1 <- cor(iris$Sepal.Length, iris$Petal.Length, method="pearson") cor1 par(mfcol = c(1,1)) plot(iris$Sepal.Length, iris$Petal.Length, main = "Sepal Length vs Petal Length", xlab = "Sepal Length", ylab = "Petal Length") ## Correlation matrix and treatmentof missing data dSet <- iris # Remove one discretevariable dSet$Species <- NULL # introduce NA in dSet$Sepal.Length[5] dSet$Sepal.Length[5] <- NA # Pairwise and Listwise Deletion: cor1a <- cor(dSet,use="complete.obs") # listwise deletion cor1a <- cor(dSet,use="pairwise.complete.obs") # pairwise deletion cor1a <- cor(dSet,use="all.obs") # all observations -error Correlation Intro to R for Data Science Session 6: Linear Regression in R
  • 8. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 library(Hmisc) cor2 <- rcorr(iris$Sepal.Length, iris$Petal.Length, type="pearson") cor2$r # correlations cor2$r[1,2] # that's whatyou need,right cor2$P # significantat cor2$n # num.observations # NOTE: rcorr uses Pairwise deletion! # Correlation matrix cor2a <- rcorr(as.matrix(dSet), type="pearson") # NOTE:as.matrix # select significant at alpha == .05 w <- which(!(cor2a$P<.05),arr.ind = T) cor2a$r[w] <- NA cor2a$P # comparew. cor2a$r Correlation {Hmisc} Intro to R for Data Science Session 6: Linear Regression in R
  • 9. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 # LinearRegression:lm() # Predicting:PetalLength from SepalLength reg <- lm(Petal.Length ~ Sepal.Length, data=iris) class(reg) summary(reg) coefsReg <- coefficients(reg) coefsReg slopeReg <- coefsReg[2] interceptReg <- coefsReg[1] # Prediction from this model newSLength <- data.frame(Sepal.Length = runif(100, min(iris$Sepal.Length), max(iris$Sepal.Length)) ) # watch the variable namesin the new data.frame! predictPLength <- predict(reg, newSLength) predictPLength Linear Regression with lm() Intro to R for Data Science Session 6: Linear Regression in R
  • 10. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 # Standardizedregressioncoefficients {QuantPsych} library(QuantPsyc) lm.beta(reg) # Reminder:standardizedregressioncoefficientsare... # What you would obtain upon performinglinearregressionoverstandardizedvariables # z-score in R zSLength <- scale(iris$Sepal.Length, center = T, scale = T) # computes z-score zPLength <- scale(iris$Petal.Length, center = T, scale = T) # again;?scale # new dSetw. standardized variables dSet <- data.frame(Sepal.Length <- zSLength, Petal.Length <- zPLength) # LinearRegression w.lm() overstandardized variables reg1 <- lm(Petal.Length ~ Sepal.Length, data=dSet) summary(reg1) # compare coefficients(reg1)[2] # beta from reg1 lm.beta(reg) # standardizedbeta w. QuantPscy lm.beta from reg Standardized Regression Coefficients Intro to R for Data Science Session 6: Linear Regression in R
  • 11. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 # plots w. {base}and {ggplot2} library(ggplot2) # Predictorvs Criterion {base} plot(iris$Sepal.Length, iris$Petal.Length, main = "Petal Length vs Sepal Length", xlab = "Sepal Length", ylab = "Petal Length" ) abline(reg,col="red") # Predictorvs Criterion {ggplot2} ggplot(data = iris, aes(x = Sepal.Length, y = Petal.Length)) + geom_point(size = 2, colour = "black") + geom_point(size = 1, colour = "white") + geom_smooth(aes(colour = "red"), method='lm') + ggtitle("Sepal Length vs Petal Length") + xlab("Sepal Length") + ylab("Petal Length") + theme(legend.position = "none") Plots {base} vs {ggplot2} Intro to R for Data Science Session 6: Linear Regression in R
  • 12. Plots {base} vs {ggplot2} Intro to R for Data Science Session 6: Linear Regression in R
  • 13. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 # Predicted vs.residuals {ggplot2} predReg <- predict(reg) # get predictions from reg resReg <- residuals(reg) # get residuals from reg # resStReg <- rstandard(reg)# get residualsfrom reg plotFrame <- data.frame(predicted = predReg, residual = resReg); ggplot(data = plotFrame, aes(x = predicted, y = residual)) + geom_point(size = 2, colour = "black") + geom_point(size = 1, colour = "white") + geom_smooth(aes(colour = "blue"), method='lm', se=F) + ggtitle("Predicted vs Residual Lengths") + xlab("Predicted Lengths") + ylab("Residual") + theme(legend.position = "none") Predicted vs Residuals Intro to R for Data Science Session 6: Linear Regression in R
  • 14. Predicted vs Residuals Intro to R for Data Science Session 6: Linear Regression in R
  • 15. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 ## Detectinfluentialcases infReg <- as.data.frame(influence.measures(reg)$infmat) # Cook's Distance:Cook and Weisberg(1982): # values greaterthan 1 are troublesome wCook <- which(infReg$cook.d>1) # we're fine here # Average Leverage = (k+1)/n,k - num. of predictors,n - num. observations # Also termed:hat values,range:0 - 1 # see: https://en.wikipedia.org/wiki/Leverage_%28statistics%29 # Various criteria (twice the leverage,three times the average...) wLev <- which(infReg$hat>2*(2/length(iris$price))) # we seem to be fine here too... ## Influenceplot infReg <- as.data.frame(influence.measures(reg)$infmat) plotFrame <- data.frame(residual = resStReg, leverage = infReg$hat, cookD = infReg$cook.d) Infulential Cases + Infulence Plot Intro to R for Data Science Session 6: Linear Regression in R
  • 16. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 ggplot(plotFrame, aes(y = residual, x = leverage)) + geom_point(size = plotFrame$cookD*100, shape = 1) + ggtitle("Influence PlotnSize of the circle corresponds to Cook's distance") + theme(plot.title = element_text(size=8, face="bold")) + ylab("Standardized Residual") + xlab("Leverage") Infulence Plot Intro to R for Data Science Session 6: Linear Regression in R
  • 17. Infulence Plot Intro to R for Data Science Session 6: Linear Regression in R