data mining with r- regression

7/27/2019 Data Mining With R- Regression

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Data Mining with RRegression models

Hamideh Iraj

[email protected]



Slides Reference

This a curation from:

Data Analysis Course

Weeks 4-5-6

https://www.coursera.org/course/dataanalysis



Galton Data – Introduction

library(UsingR)

data(galton)

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Head(galton)

Tail(galton)

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Dim(galton)

Str(galton)

summary(galton)

summary(galton$child)



Galton Data - Plotting

par(mfrow=c(1,2))

hist(galton$child,col="blue",breaks=100)

hist(galton$parent,col="blue",breaks=100)



Galton Data – Plotting - cont.

pairs(galton)



What is Regression Analysis?

regression analysis is a statistical process for estimating therelationships among variables. It includes many techniques formodeling and analyzing several variables, when the focus is on threlationship between a dependent variable and one ormore independent variables.

http://en.wikipedia.org/wiki/Regression_analysis



Fitting a line

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

lm1 <- lm(child ~ parent, data=galton)

lines(galton$parent,lm1$fitted,col="red", lwd=3)

The linewidth



Plot Residuals

plot(galton$parent,lm1$residuals,col="blue",pch=19)

Abline (c(0,0),col="red",lwd=3)



Linear Model Coefficients

>Summary(lm1)

lm1$coeff



Why care about model Accuracy?

http://en.wikipedia.org/wiki/Linear_regression



Model Accuracy Measures

P-value

Confidence Interval

R2

Adjusted R2



P-value

Most Common Measure of Statistical Significance

Idea: Suppose nothing is going on - how unusual is it to see the estimate we go

Some typical values (single test)

P < 0.05 (significant)

P < 0.01 (strongly significant)

P < 0.001 (very significant)



Confidence intervals

A confidence interval is a type of interval estimate of a populatioparameter and is used to indicate the reliability of an estimate

confint(lm1,level=0.95)

http://en.wikipedia.org/wiki/Confidence_interval



R2

R2 : the proportion of response variation "explained" by theregressors in the model.

R2= 1 :the fitted model explains all variability in

R2 = 0 indicates no 'linear' relationship (for straight line regressionthis means that the straight line model is a constant line (slope=0intercept=\bar{y}) between the response variable and regressors)

http://en.wikipedia.org/wiki/Coefficient_of_determination



Adjusted R2

The use of an adjusted R2 (often written as \bar R^2 and pronounc

"R bar squared") is an attempt to take account of the phenomeno

of the R2 automatically and spuriously increasing when extra

explanatory variables are added to the model.

http://en.wikipedia.org/wiki/Coefficient_of_determination



Predicting with Linear Regression

coef(lm1)[1] + coef(lm1)[2]*80

newdata <- data.frame(parent=80)predict(lm1,newdata)



Multivariate Linear Regression

WHO childhood hunger data

Dataset:http://apps.who.int/gho/athena/data/GHO/WHOSIS_000008.csv?ofile=text&filter=COUNTRY:*

hunger <- read.csv("./hunger.csv")

hunger <- hunger[hunger$Sex!="Both sexes", ]



Multivariate Linear Regression – cont.

lmBoth <- lm(hunger$Numeric ~ hunger$Year + hunger$Sex)

lmBoth2 <- lm(hunger$Numeric ~ hunger$Year + hunger$Sex +hunger$Sex*hunger$Year)

Same slopes

Differentslopes



Model Selection

step(lmBoth2)



Regression with Factor Variables

Outcome is still quantitative

Covariate(s) are factor variables

Fitting lines = fitting means

Want to evaluate contribution of all factor levels at once



Regression with Factor Variables – cont.

Dataset: http://www.rossmanchance.com/iscam2/data/movies03RT.txt

movies <- read.table("./movies.txt",sep="\t",header=T,quote="")

head(movies)



Regression with Factor Variables – cont.

lm2 <- lm(movies$score ~ as.factor(movies$rating))

summary(lm2)

data mining with r- regression

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