Introduction to R for Data Science :: Session 6 [Linear Regression in R]
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This document provides an introduction to linear regression in R. It covers exploratory data analysis of the iris data set, correlation analysis, linear regression using lm(), plotting regression results, and identifying influential cases. Key steps include examining assumptions, fitting a linear regression model to predict petal length from sepal length, interpreting regression coefficients, and checking for high leverage or influential points. The document demonstrates many linear regression procedures in base R and with additional packages like ggplot2, Hmisc, and QuantPsyc.
![# 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$Sepal.Length[5] <- NA
# Pairwise and Listwise Deletion:
cor1a <- cor(dSet,use="complete.obs") # listwise deletion
cor1a <- cor(dSet,use="pairwise.complete.obs") # pairwise deletion
cor1a <- cor(dSet,use="all.obs") # all observations -error
Correlation
Intro to R for Data Science
Session 6: Linear Regression in R](https://image.slidesharecdn.com/intrordatasciencesession6eng-160606173046/85/Introduction-to-R-for-Data-Science-Session-6-Linear-Regression-in-R-7-320.jpg)
![# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
library(Hmisc)
cor2 <- rcorr(iris$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$r
Correlation {Hmisc}
Intro to R for Data Science
Session 6: Linear Regression in R](https://image.slidesharecdn.com/intrordatasciencesession6eng-160606173046/85/Introduction-to-R-for-Data-Science-Session-6-Linear-Regression-in-R-8-320.jpg)
![# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# LinearRegression:lm()
# Predicting:PetalLength from SepalLength
reg <- lm(Petal.Length ~ Sepal.Length, data=iris)
class(reg)
summary(reg)
coefsReg <- coefficients(reg)
coefsReg
slopeReg <- coefsReg[2]
interceptReg <- coefsReg[1]
# Prediction from this model
newSLength <- data.frame(Sepal.Length = runif(100,
min(iris$Sepal.Length),
max(iris$Sepal.Length))
) # watch the variable namesin the new data.frame!
predictPLength <- predict(reg, newSLength)
predictPLength
Linear Regression with lm()
Intro to R for Data Science
Session 6: Linear Regression in R](https://image.slidesharecdn.com/intrordatasciencesession6eng-160606173046/85/Introduction-to-R-for-Data-Science-Session-6-Linear-Regression-in-R-9-320.jpg)
![# Introduction to R for Data Science
# SESSION 6 :: 02 June, 2016
# Standardizedregressioncoefficients {QuantPsych}
library(QuantPsyc)
lm.beta(reg)
# Reminder:standardizedregressioncoefficientsare...
# What you would obtain upon performinglinearregressionoverstandardizedvariables
# z-score in R
zSLength <- scale(iris$Sepal.Length, center = T, scale = T) # computes z-score
zPLength <- scale(iris$Petal.Length, center = T, scale = T) # again;?scale
# new dSetw. standardized variables
dSet <- data.frame(Sepal.Length <- zSLength,
Petal.Length <- zPLength)
# LinearRegression w.lm() overstandardized variables
reg1 <- lm(Petal.Length ~ Sepal.Length, data=dSet)
summary(reg1)
# compare
coefficients(reg1)[2] # beta from reg1
lm.beta(reg) # standardizedbeta w. QuantPscy lm.beta from reg
Standardized Regression Coefficients
Intro to R for Data Science
Session 6: Linear Regression in R](https://image.slidesharecdn.com/intrordatasciencesession6eng-160606173046/85/Introduction-to-R-for-Data-Science-Session-6-Linear-Regression-in-R-10-320.jpg)
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Introduction to R for Data Science :: Session 6 [Linear Regression in R]
- 1. Introduction to R for Data Science Lecturers dipl. ing Branko Kovač Data Analyst at CUBE/Data Science Mentor at Springboard Data Science zajednica Srbije [email protected] dr Goran S. Milovanović Data Scientist at DiploFoundation Data Science zajednica Srbije [email protected] [email protected]
- 2. Linear Regression in R • Exploratory Data Analysis • Assumptions of the Linear Model • Correlation • Normality Tests • Linear Regression • Prediction, Confidence Intervals, Residuals • Influential Cases and the Influence Plot Intro to R for Data Science Session 6: Linear Regression in R
- 3. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 # clear rm(list=ls()) #### read data library(datasets) data(iris) ### iris data set description: # https://stat.ethz.ch/R-manual/R-devel/library/iriss/html/iris.html ### ExploratoryData Analysis (EDA) str(iris) summary(iris) Linear Regression in R • Before modeling: Assumptions and Exploratory Data Analysis (EDA) Intro to R for Data Science Session 6: Linear Regression in R
- 4. # Introduction to R for Data Science # SESSION 6 :: 02 June, 2016 ### EDA plots # plot layout:2 x 2 par(mfcol = c(2,2)) # boxplotiris$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