LinearRegression: Linear Regression

In Harrindy/StatEngine: An R Package for the UofSC Course STAT 509 "Statistics for Engineers"

Description

Inferences for linear regression: confidence intervals and hypthesis testing on regression coefficients, confidence interval on the mean response at a given x and prediction interval on a future observation at a given x, Partial F-test, model adequacy checking.

Usage

# fit must be an lm object; e.g., fit=lm(y~x).
lm.est(fit)

# based on the fit, compute CIs and tests on betas
lm.coef.CI(fit,level=0.95)
# The default value of hypo.beta is zero
lm.coef.test(fit,alpha=0.05,H1="two",hypo.beta=?)

#Partial F-test,
#fit.H0 is the lm object using the null model
#fit.ALL is the lm object using the full model
lm.partialFtest(fit.H0=lmH0,fit.ALL=lmALL,alpha=0.05)

# Model Adequacy checking
lm.modelcheck(fit)
# fit must be an lm object. VIFs are also printed.

Arguments

fit	an lm object
level	the confidence level
alpha	the significance level
hypo.beta	the hypothesized beta value that about to be tested
fit.H0, fit.ALL	the null model and full model in the partial F-test

Details

Inferences for linear regression: confidence intervals and hypthesis testing on regression coefficients, confidence interval on the mean response at a given x and prediction interval on a future observation at a given x, Partial F-test, model adequacy checking.

Value

lm.est	the least squares estimates
interval	As long as the function has "interval", the outcome are confidence intervals.
test	As long as the function has "test", it conduct the hypothesis testing.
lm.modelcheck	residual analysis and VIFs

Note

[e-mail]

Author(s)

Dewei Wang

References

Chapters 11-12 of the textbook "Applied Statistics and Probability for Engineers" 7th edition

Examples

Example1=read.csv("https://raw.githubusercontent.com/Harrindy/StatEngine/master/Data/HydrocarbonPurity.csv")
x=Example1$HydrocarbonLevels
y=Example1$Purity
fit=lm(y~x)
lm.est(fit)
summary(fit)
lm.coef.interval(fit,level=0.95)
predict.lm(fit,new=data.frame(x=1),interval="confidence")
predict.lm(fit,new=data.frame(x=1),interval="prediction")


Example2=read.csv("https://raw.githubusercontent.com/Harrindy/StatEngine/master/Data/WireBond.csv")
head(Example2,2)
y=Example2$PullStrength
x1=Example2$WireLength
x2=Example2$DieHeight
fit=lm(y~x1+x2)
summary(fit)
lm.coef.interval(fit,level=0.95)
lm.coef.test(fit,alpha=0.05,H1="two")
predict.lm(fit,new=data.frame(x1=8,x2=275),interval="confidence")
predict.lm(fit,new=data.frame(x1=8,x2=275),interval="prediction")
data.summary(fit$residuals)
vif(fit)
lm.modelcheck(fit)

x3=x1^2
x4=x2^2
lmH0=lm(y~x1+x2)
lmALL=lm(y~x1+x2+x3+x4)
lm.partialFtest(fit.H0=lmH0,fit.ALL=lmALL,alpha=0.05)
summary(lm(y~x1+x2+x3))
summary(lm(y~x1+x2+x4))
summary(lm(y~x1+x2+x3+x4))

Example3=read.csv("https://raw.githubusercontent.com/Harrindy/StatEngine/master/Data/AirplaneSidewallPanels.csv")
head(Example3,2)
y=Example3$cost
x=Example3$lotsize
plot(x,y)
fit=lm(y~x)
lines(x,fit$fitted.values)
x2=x^2
fit.quad=lm(y~x+x2)
lines(x,fit.quad$fitted.values,col="blue")
summary(fit)
summary(fit.quad)


Example4=read.csv("https://raw.githubusercontent.com/Harrindy/StatEngine/master/Data/SurfaceFinishData.csv")
head(Example4,2)
plot(Example4)
y=Example4$SurfaceFinish
x1=Example4$RPM
x2=Example4$TypeofCuttingTool
fit=lm(y~x1+x2)
summary(fit)
par(mar=c(4,4,.1,.1))
par(mfrow=c(1,2))
plot(x1[x2==0],y[x2==0])
lines(x1[x2==0],fit$fitted.values[x2==0])
plot(x1[x2==1],y[x2==1])
lines(x1[x2==1],fit$fitted.values[x2==1])

x3=x1*x2
fit2=lm(y~x1+x2+x3)
summary(fit2)
par(mfrow=c(1,1))
plot(x1,y)
lines(x1[x2==0],fit$fitted.values[x2==0])
lines(x1[x2==1],fit$fitted.values[x2==1])
lines(x1[x2==0],fit2$fitted.values[x2==0],col="blue")
lines(x1[x2==1],fit2$fitted.values[x2==1],col="blue")

Harrindy/StatEngine documentation built on Nov. 19, 2021, 1:10 p.m.