DAA09

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2 > summary(dat.lm1) Call: lm(formula = sales ~ price, data = dat) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-12 *** price e-06 *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: 26 on 48 degrees of freedom Multiple R-squared: ,Adjusted R-squared: F-statistic: on 1 and 48 DF, p-value: 8.486e-06

3 > dat.lm2 <- lm(sales~price+material,data = dat) > summary(dat.lm2) Call: lm(formula = sales ~ price + material, data = dat) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-11 *** price e-05 *** material Signif. codes: 0 *** ** 0.01 * Residual standard error: on 47 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 47 DF, p-value: 4.578e-05

4 > dat.regall<-lm(sales~.,data=dat) > summary(dat.regall) Residual standard error: 17 on 46 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 3 and 46 DF, p-value: 3.874e-13 σ 1 σ 2! " # :;<= *+,(./012) 5 *+,(1,,/,) = 66> 5 08<??:?! # # ~% & ',& : : *+,./012 = *+,(1,,/,) E 66> = B CD" F C HF C # 667 = B C F C F #

5 ! " # = 0, ( ), *+ = ), *, ( cov " #, " 0 = 0, (, 1 "~3 0, ) *! 4 6 =! : 6 + " 6 =! ! 7 : 6 6 +! " 6 = : 6 VAR 4 6 = VAR : 6 + " 6 = VAR " 6 = ) *, 4~ : 6, ) * 6

6 dat<-read.csv(" dat.lm01<-lm(sales~price, data=as.data.frame(scale(dat))) Residuals vs Fitted >plot(dat.lm01,which=1)! " # = 0, ( ), *+ = ), *, ( Residuals Fitted values lm(sales ~ price)

7 >plot(dat.lm01,which=2) Normal Q-Q!~# 0, & ' Standardized residuals Theoretical Quantiles lm(sales ~ price)

8 norm.vars=rnorm(300) qqnorm(norm.vars) qqline(norm.vars,col='red',lwd=2) Normal Q-Q Plot unif.vars=runif(300) qqnorm(unif.vars) qqline(unif.vars,col='green',lwd=2) Normal Q-Q Plot Sample Quantiles Sample Quantiles Theoretical Quantiles Theoretical Quantiles

9 > plot(sort(unif.vars),sort(unif.vars)) sort(unif.vars) > plot(sort(norm.vars),sort(unif.vars)) sort(unif.vars) sort(unif.vars) sort(norm.vars)

10 par(mfrow=c(2,2)) plot(dat.lm01) Residuals Residuals vs Fitted Standardized residuals Normal Q-Q Fitted values Theoretical Quantiles Standardized residuals Scale-Location Standardized residuals Residuals vs Leverage Cook's distance Fitted values Leverage

11 dat<-read.csv(" > levels(dat$method) [1] "free" "image" "repeat" "sentence" # factor dat$method=factor(dat$method, levels(dat$method)[c(1,3,4,2)]) > levels(dat$method) [1] "free" "repeat" "sentence" "image"

12 Residuals vs Fitted Normal Q-Q > dat.lm<-lm(result~method,data=dat) > par(mfrow=c(2,2)) > plot(dat.lm) Residuals Standardized residuals Fitted values Theoretical Quantiles Standardized residuals Scale-Location Standardized residuals Constant Leverage: Residuals vs Factor Levels 8 method : free repeat image Fitted values Factor Level Combinations

13 ! " = $ " &$ " = $ " ' ( ' ) * "! " =, -. )/0 - h " = ) / / 4 6

15 > dat <- read.csv(" > summary(dat) material price design sales Min. : 1.00 Min. :100.0 Min. :10.00 Min. : st Qu.: st Qu.: st Qu.: st Qu.: 99.0 Median : 5.00 Median :145.0 Median :39.00 Median :106.5 Mean : 5.22 Mean :144.3 Mean :39.12 Mean : rd Qu.: rd Qu.: rd Qu.: rd Qu.:127.5 Max. :10.00 Max. :195.0 Max. :70.00 Max. :203.0 > dat2 <- rbind(dat,c(0,0,100,250)) > tail(dat2) material price design sales plot(dat2,col=c(rep("black",50),"red"),pch=20,cex=3)

17 > dat.lm<-lm(sales~design,data=dat) > summary(dat.lm) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-07 *** design Signif. codes: 0 *** ** 0.01 * Residual standard error: 31.1 on 48 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 48 DF, p-value: > dat2.lm<-lm(sales~design,data=dat2) > summary(dat2.lm) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-06 *** design *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 49 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 49 DF, p-value:

18 ! #! # = % 1 h #

19 !""#$%&' ( = $ ( = * +, -* +. / , ( = , /

20 b = ( X T X) 1 X T y

21 dat<-read.csv(" plot(dat) >dat.lm<-lm(sales~., data=dat) material price design sales dump

22 material > summary(dat.lm) Call: lm(formula = sales ~., data = dat) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-13 *** material e-05 *** price e-06 *** design e-07 *** dump * --- Signif. codes: 0 *** ** 0.01 * price design sales dump Residual standard error: on 29 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 4 and 29 DF, p-value: 9.846e-09

23 VIF i = 1-1 R 2 i

24 dat.lm<-lm(sales~., data=dat) install.packages("daag") library(daag) vif(dat.lm) material price design dump lm.price<-lm(price~material+design+dump, data=dat) p.rsq = summary(lm.price)$r.squared vif.p = 1/(1-p.rsq) > vif.p [1]

25 > dat<-read.csv(" > head(dat) grade study study.sq study.type g g g g g g2

26 Polynomial regression > poly.lm<-lm(grade~study+study.sq, data= dat) > summary(poly.lm) Call: lm(formula = grade ~ study + study.sq, data = dat) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) * study e-13 *** study.sq e-08 *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 47 degrees of freedom Multiple R-squared: 0.905, Adjusted R-squared: F-statistic: on 2 and 47 DF, p-value: < 2.2e-16

27 Polynomial regression plot(grade~study,data=dat,pch=20,xlab = "hours studied",xlim=c(3,27), ylim =c(0,110),cex=2) x = seq(0,30,0.1) y = *x *x^2 lines(x,y,col='red',lwd=3)

30 dat<-read.table(" plot(dat,pch=20,cex=2)

31 Absence = b 1 Interest + e 1 Study = b 2 Interest + b 3 Knowledge + e 2 Grade = b 4 Knldg.+ b 5 Ab.+ b 6 Std.+ e 3 b1 b2 b3 b4 b5 b6

32 dat<-read.table(" dat.lm1<-lm(absence~interest,dat) > summary(dat.lm1) Call: lm(formula = absence ~ interest, data = dat) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) < 2e-16 *** interest e-13 *** --- Signif. codes: 0 *** ** 0.01 *

33 dat.lm2<-lm(study~interest+knowledge,dat) > summary(dat.lm2) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) ** interest e-15 *** knowledge *** dat.lm3<-lm(grade~knowledge+study+absence,dat) > summary(dat.lm3) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-07 *** knowledge *** study *** absense e-06 ***

35 dat.std<-as.data.frame(scale(dat)) > summary(dat.std) interest knowledge absence study grade Min. : Min. : Min. : Min. : Min. : st Qu.: st Qu.: st Qu.: st Qu.: st Qu.: Median : Median : Median : Median : Median : Mean : Mean : Mean : Mean : Mean : rd Qu.: rd Qu.: rd Qu.: rd Qu.: rd Qu.: Max. : Max. : Max. : Max. : Max. : > var(dat.std) interest knowledge absence study grade interest knowledge absence study grade

36 > summary(lm(absence~interest,dat.std)) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 5.658e e interest e e e-13 *** > summary(lm(study~interest+knowledge,datstd)) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e e e interest 9.272e e e-15 *** knowledge e e *** > summary(lm(grade~study+absence+knowledge,datstd)) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 1.822e e e study 3.100e e *** absence e e e-06 *** knowledge 2.727e e ***

Use R

Use R Use R! 2008/05/23( ) Index Introduction (GLM) ( ) R. Introduction R,, PLS,,, etc. 2. Correlation coefficient (Pearson s product moment correlation) r = Sxy Sxx Syy :, Sxy, Sxx= X, Syy Y 1.96 95% R cor(x,