Nothing
inst/SimpleLMApp.r
In lmviz: A Package to Visualize Linear Models Features and Play with Them
#library(shiny)
#library(shinyjs)
ui <- fluidPage(
shinyjs::useShinyjs(),
withMathJax(),
# tags$img(width=300,height=50,src="deams.png"),
# tags$img(width=300,height=50,src="logoUnits2.jpg"),
h1("Simple linear regression"),
#tabsetPanel(
# tabPanel("a",
# Input functions
sidebarLayout(
sidebarPanel(
sliderInput("n","Number of observations",min=8,max=1000,value=25,step=1),
hr(),
p(strong("Model: \\(y_i=\\beta_1+\\beta_2x_i+\\varepsilon_i\\), \\(\\varepsilon_i\\thicksim IID(\\mathcal N(0,\\sigma^2))\\)")),
splitLayout(
numericInput("beta0","\\(\\beta_1\\)",0,-10,10,0.1,width="100%"),
numericInput("beta1","\\(\\beta_2\\)",1,-10,10,0.1,width="100%"),
numericInput("sdeverr","\\(\\sigma\\)",1,0,10,0.1,width="100%")
),
hr(),
p(strong("Explanatory variable")),
splitLayout(
numericInput("sdevx","\\(\\sqrt{V(x)}\\)",0.5,0,1,0.1,width="100%"),
numericInput("xbar","\\(\\bar{x}\\)",0,-3,3,0.1,width="100%")
),
checkboxInput("mostra","show estimates on plot"),
hr(),
actionButton("aggiorna","Draw Y"),
p("A new sample for Y is drawn based on the input parameters."),
actionButton("aggiorna2","Draw Y repeatedly"),
p("A new simulation will be drawn every 0.5/0.1 seconds"),
hr(),
p("Sample distributions and c.i. plots are reset if any parameter is changed."),
hr(),
actionButton("scarica","Download data"),
p("Saves data in temp.csv in the working directory")
),
mainPanel(
fluidRow(
column(width = 8,{
verticalLayout(
plotOutput("scatter")
)
}),
column(width = 4,
wellPanel(
plotOutput("stim")
))
),
tabsetPanel(
tabPanel("Residuals",
splitLayout(
plotOutput("residui1", width = "100%"),
plotOutput("residui2", width = "100%"),
plotOutput("residui3", width = "100%")
)
),
tabPanel("Sample dist. coefs",
splitLayout(
plotOutput("beta0plot", width = "100%"),
plotOutput("beta1plot", width = "100%"),
plotOutput("beta0beta1", width = "100%")
),
textOutput("numsim")
),
tabPanel("Conf. int.",
splitLayout(
wellPanel(
numericInput("livconf","Confidence level",0.95,0.5,0.999,0.001,width="100%"),
p("Do not cover the true value"),
p(textOutput("beta0ictesto")),
p(textOutput("beta1ictesto"))
),
plotOutput("beta0ic", width = "100%"),
plotOutput("beta1ic", width = "100%")
)
),
tabPanel("Sample dist var",
splitLayout(
plotOutput("sigmaplot", width = "100%"),
plotOutput("sigma2plot", width = "100%")
),
textOutput("numsim2")
),
tabPanel("Piv. Q.",
splitLayout(
plotOutput("qp1plot", width = "100%"),
plotOutput("qp2plot", width = "100%")
),
textOutput("numsim3")
),
tabPanel("Prediction",
splitLayout(
wellPanel(
verticalLayout(
checkboxInput("previsioni","Show predictions on plot"),
sliderInput("livello","Level",0.5,0.99,0.90,0.01,width="100%"),
sliderInput("extra","extrapolation (%)",0,200,0,1,width="100%")
)),
plotOutput("previsioniv")
)
)
)
)
# p("Prova a inventare un insieme di osservazioni che corrisponda al diagrama a scatola disegnato sopra."),
# textInput('vec1', 'Inserisci le osservazioni separate da , (usa il . per i decimali)', ""),
# Ouptut functions
# actionButton("invio","Invia"),
# plotOutput("boxplot2", width = "66%")
)
)
# textOutput("qq1")),
nintf=function(x) {
if (length(x)<50) 5
if ((length(x)>=50) & (length(x)<500)) 20
if ((length(x)>=500)) 30
}
server <- function(input, output, session) {
# input$<id> available
# data <- reactive ({}) #respond to every value in input, to be used as data()
# output$<nomeoutput> <- render<TIPO>({ <codice> })
rv=reactiveValues()
rv$beta0.v=c()
rv$beta1.v=c()
rv$sigma.v=c()
rv$sd.v=c()
fit=reactive({fit=lm(y()~x())})
summfit=reactive({summary(fit())})
tempo=reactiveVal(30000000000000000)
observeEvent(input$aggiorna2,{
if ((input$aggiorna2 %% 3)==0){
tempo(30000000000000000)
updateActionButton(session, "aggiorna2",label="Draw Y repeatedly")
} else {
if ((input$aggiorna2 %% 3)==1){
tempo(500)
updateActionButton(session, "aggiorna2",label="Accelerate drawings")
} else {
tempo(50)
updateActionButton(session, "aggiorna2",label="Stop automatic drawings")
}
}
})
observe({
shinyjs::click("aggiorna")
invalidateLater(tempo())
})
observeEvent(y(),{
temp=rv$beta1.v
temp=c(temp,fit()$coefficients[2])
rv$beta1.v=temp
temp=rv$beta0.v
temp=c(temp,fit()$coefficients[1])
rv$beta0.v=temp
temp=rv$sigma.v
temp=c(temp,sum(fit()$resid^2)/(input$n-2))
rv$sigma.v=temp
})
observeEvent(input$n*input$beta0*input$beta1*input$sdeverr*input$sdevx*input$xbar,{
rv$beta1.v=c()
rv$beta0.v=c()
rv$sigma.v=c()
})
observeEvent(input$scarica,{
#dati=data.frame(x=x(),y=y())
#.GlobalEnv$results.SimpleLM=dati
write.table(dati,sep=",",file=paste0(.wd,"/temp.csv"))
})
output$numsim=renderText(
paste("Sample distributions of estimators based on ",
length(rv$beta1.v),
"simulations; green: true values, gray: theorical distribution, triangle: mean of simulated estimates.")
)
output$numsim2=renderText(
paste("Sample distributions of estimators based on ",
length(rv$beta1.v),
"simulations; green: true values, gray: theorical distribution.")
)
output$numsim3=renderText(
paste("Sample distributions of pivotal quantities based on",
length(rv$beta1.v),
"simulations; green: theorical distribution.")
)
output$stim=renderPlot({
req(is.numeric(input$beta1))
par(mar=c(1,1,1,1),cex=1.5)
plot(c(0,1),c(1.5,9),type="n",bty="n",xaxt="n",yaxt="n",xlab="n",ylab="n")
text(0,9,adj=c(0,1),col="darkred",
label=substitute(paste(hat(beta)[1],"=",b0),
list(b0=signif(fit()$coef[1],3),vb1=signif(summfit()$coefficients[1,2],3))))
text(0,8,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(hat(v)(hat(beta)[1])),"=",vb1),
list(b0=signif(fit()$coef[1],3),vb1=signif(summfit()$coefficients[1,2],3))))
text(0,7,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(v(hat(beta)[1])),"=",vb1v),
list(vb1v=signif(input$sdeverr*sqrt(1/input$n+input$xbar^2/Dx()),3))))
text(0,6,adj=c(0,1),col="darkred",
label=substitute(paste(hat(beta)[2],"=",b1),
list(b1=signif(fit()$coef[2],3))))
text(0,5,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(hat(v)(hat(beta)[2])),"=",vb2),
list(b1=signif(fit()$coef[1],3),vb2=signif(summfit()$coefficients[2,2],3))))
text(0,4,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(v(hat(beta)[2])),"=",vb1v),
list(vb1v=signif(input$sdeverr*sqrt(1/Dx()),3))))
text(0,3,adj=c(0,1),col="darkred",
label=substitute(paste(s^2,"=",s2," (s=",ss,")"),
list(s2=signif(summfit()$sigma^2,3),ss=signif(summfit()$sigma,3))))
text(0,2,adj=c(0,1),col="darkred",
label=substitute(paste(R^2,"=",r2),
list(r2=signif(summfit()$r.squared,3))))
})
x=eventReactive(input$n*input$sdevx*input$xbar,{
req(is.numeric(input$xbar) & is.numeric(input$sdevx) & (input$sdevx>0))
x=rnorm(input$n,0,1)
x=(x-mean(x))/sd(x)
x=input$xbar+input$sdevx*x
return(x)
})
Dx=reactive({sum((x()-input$xbar)^2)})
y=eventReactive(
input$aggiorna*input$n*input$beta0*input$beta1*input$sdeverr*input$sdevx*input$xbar, {
req(is.numeric(input$beta1) & is.numeric(input$beta0)& is.numeric(input$sdeverr) & (input$sdeverr>0))
#autoInvalidate()
y=input$beta0+input$beta1*x()+rnorm(input$n,0,input$sdeverr)
return(y)
},ignoreNULL = FALSE)
output$scatter=renderPlot({
par(mar=c(4,4,1,1))
if (input$mostra){
limx=c(min(c(0,1,x())),max(c(0,1.1,x())))
limy=range(c(input$beta0+input$beta1*(input$xbar+c(-1,1)*4*input$sdevx)+c(-1,1)*3*input$sdeverr,input$beta0+c(-1,1)*qnorm(0.95)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),input$beta0+c(-1,1,-1,1)*qnorm(0.95)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())+input$beta1+c(-1,-1,1,1)*qnorm(0.95)*input$sdeverr*sqrt(1/Dx())))
} else {
limx=c(min(x()),max(x()))
limy=range(input$beta0+input$beta1*(input$xbar+c(-1,1)*4*input$sdevx))+c(-1,1)*3*input$sdeverr
}
if (input$previsioni){
updateCheckboxInput(session, "mostra",value=FALSE)
limx=c(min(x())-(input$extra/200)*(max(x())-min(x())),max(x())+(input$extra/200)*(max(x())-min(x())))
limy=range(c(input$beta0+input$beta1*limx[1]+c(-1,1)*qt(0.99,5)*input$sdeverr*sqrt(1+1/input$n+(limx[1]-input$xbar)^2/Dx()),
input$beta0+input$beta1*limx[2]+c(-1,1)*qt(0.99,5)*input$sdeverr*sqrt(1+1/input$n+(limx[2]-input$xbar)^2/Dx())
))
}
a=plot(x(),y(),xlim=limx,
ylim=limy,las=1,xlab="x",ylab="y",las=1,pch=20,yaxt="n",bty="n")
axis(1,at=c(limx[1]-1,limx[2]+1),labels=c("",""))
axis(2,las=1,
at=c(limy[1]-4,limy[2]+4),
labels=c("",""))
axis(2,las=1,
at=c(limy,input$beta0),
labels=signif(c(limy,input$beta0),3))
rug(x())
text(ifelse(input$beta1>0,limx[1],limx[2]),limy[2],adj=c(0+(input$beta1<=0),1),col="darkred",
label=substitute(paste(hat(y),"=",b0,segno,b1,"x"," (est. reg. line)"),
list(b0=signif(fit()$coef[1],3),b1=signif(fit()$coef[2],3),r2=signif(summfit()$r.squared,3),segno=ifelse(fit()$coef[2]>0,"+","")))
)
text(ifelse(input$beta1>0,limx[1],limx[2]),limy[2]-0.1*(limy[2]-limy[1]),adj=c(0+(input$beta1<=0),1),col="darkgray",
label=substitute(paste(E(y),"=",b0,segno,b1,"x"," (true reg. line)"),
list(b0=signif(input$beta0,3),b1=signif(input$beta1,3),segno=ifelse(input$beta1>0,"+","")))
)
# expression(paste("Retta stimata:",hat(y),"=",signif(fit()$coef[1],3)," + ",signif(fit()$coef[2],3),"x")))
curve(input$beta0+input$beta1*x,col=gray(0.5),lwd=2,add=TRUE)
curve(fit()$coef[1]+fit()$coef[2]*x,col="darkred",lwd=2,add=TRUE)
if (input$mostra){
par(xpd=NA)
text(0,fit()$coef[1],adj=c(fit()$coef[2]>=0,0),
labels=expression(hat(beta)[1]),col="darkgreen",cex=1.5)
text(1,mean(c(fit()$coef[1],fit()$coef[1]+fit()$coef[2])),pos=4,labels=expression(hat(beta)[2]),col="darkgreen",cex=1.5)
par(xpd=FALSE)
points(0,fit()$coef[1],pch=20,cex=1.5,col="darkgreen")
abline(v=c(0,1),lty=2)
segments(1,fit()$coef[1],1,fit()$coef[1]+fit()$coef[2],lwd=2,col="darkgreen")
segments(0,fit()$coef[1],1,fit()$coef[1],lty=2)
}
if (input$previsioni){
xseq=seq(limx[1],limx[2],length=100)
polygon(c(xseq,rev(xseq)),c(fit()$coef[1]+fit()$coef[2]*xseq+qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1/input$n+(xseq-input$xbar)^2/Dx()),fit()$coef[1]+fit()$coef[2]*rev(xseq)-qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1/input$n+(rev(xseq)-input$xbar)^2/Dx())),border=NA,col="#8C000069")
curve(fit()$coef[1]+fit()$coef[2]*x+qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1+1/input$n+(x-input$xbar)^2/Dx()),add=TRUE,lwd=2,col="darkred",lty=3)
curve(fit()$coef[1]+fit()$coef[2]*x-qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1+1/input$n+(x-input$xbar)^2/Dx()),add=TRUE,lwd=2,col="darkred",lty=3)
}
})
output$beta1plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(rv$beta1.v,n=nintf(rv$beta1.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(beta)[2]),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dnorm(input$beta1,input$beta1,input$sdeverr*sqrt(1/Dx())))))
points(input$beta1,0,pch=20,col="darkgreen",cex=3)
points(mean(rv$beta1.v),0,pch=17,col="black",cex=2.2)
curve(dnorm(x,input$beta1,input$sdeverr*sqrt(1/Dx())),add=TRUE,col=gray(0.7),lwd=2)
})
output$beta0plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(rv$beta0.v,n=nintf(rv$beta0.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(beta)[1]),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dnorm(input$beta0,input$beta0,input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())))))
points(input$beta0,0,pch=20,col="darkgreen",cex=3)
points(mean(rv$beta0.v),0,pch=17,col="black",cex=2.2)
curve(dnorm(x,input$beta0,input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())),add=TRUE,col=gray(0.7),lwd=2)
})
output$qp1plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
qp=(rv$beta0.v-input$beta0)/(rv$sigma.v*sqrt(1/input$n+input$xbar^2/Dx()))
a= hist(qp,n=nintf(qp))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(t[1]),freq=FALSE,
xlim=range(c(qt(c(0.001,0.999),df=input$n-2),qp)),ylim=c(0,max(1.2*dt(0,df=input$n-2),0*a$density)))
curve(dt(x,df=input$n-2),add=TRUE,col="darkgreen",lwd=2)
})
output$qp2plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
qp=(rv$beta1.v-input$beta1)/(rv$sigma.v*sqrt(1/Dx()))
a= hist(qp,n=nintf(qp))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(t[2]),freq=FALSE,
xlim=range(c(qt(c(0.001,0.999),df=input$n-2),qp)),ylim=c(0,max(1.2*dt(0,df=input$n-2),0*a$density)))
curve(dt(x,df=input$n-2),add=TRUE,col="darkgreen",lwd=2)
})
output$beta0beta1=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,5,1,1))
plot(rv$beta0.v,rv$beta1.v,pch=20,col="darkred",xlab=expression(hat(beta)[1]),ylab=expression(hat(beta)[2]),las=1)
points(input$beta0,input$beta1,pch=20,col="darkgreen",cex=2)
})
output$previsioniv=renderPlot({
par(mar=c(5,4,0.5,0.5))
limx=c(min(x()),max(x()))
if (input$previsioni){
limx=c(min(x())-(input$extra/200)*(max(x())-min(x())),max(x())+(input$extra/200)*(max(x())-min(x())))
}
matplot(matrix(rep(limx,length(rv$beta0.v)),nrow=2),
rbind(rv$beta0.v+rv$beta1.v*limx[1],rv$beta0.v+rv$beta1.v*limx[2]),type="l",lty=1,col="#8C000069",
xlab="x",ylab="y")
abline(c(input$beta0,input$beta1),col=gray(0.25),lwd=2)
})
output$sigmaplot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(sqrt(rv$sigma.v),n=nintf(rv$sigma.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(sigma)),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dchisq(input$n-2,input$n-2)*2*sqrt(input$sdeverr^2)*(input$n-2)/input$sdeverr^2)))
points(input$sdeverr,0,pch=20,col="darkgreen",cex=3)
curve(dchisq(x^2*(input$n-2)/input$sdeverr^2,input$n-2)*2*x*(input$n-2)/input$sdeverr^2,col=gray(0.7),lwd=2,add=TRUE)
})
output$sigma2plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(rv$sigma.v,n=nintf(rv$sigma.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(sigma)^2),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dchisq(input$n-2,input$n-2)*(input$n-2)/input$sdeverr^2)))
points(input$sdeverr^2,0,pch=20,col="darkgreen",cex=3)
curve(dchisq(x*(input$n-2)/input$sdeverr^2,input$n-2)*(input$n-2)/input$sdeverr^2,col=gray(0.7),lwd=2,add=TRUE)
})
output$beta0ic=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
plot(rv$beta0.v,1:length(rv$beta1.v),
bty="n",
yaxt="n",
xaxt="n",
xlim=c(input$beta0-2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),
input$beta0+2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())),
ylim=c(0,max(100,length(rv$beta1.v))),
xlab=expression(hat(beta)[1]))
axis(1,at=signif(c(input$beta0-4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),
input$beta0+c(-1,1,-0.5,0.5)*2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),
input$beta0,
input$beta0+4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())),2))
abline(v=input$beta0,col=gray(0.8),lwd=2)
segments(rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()),
1:length(rv$beta0.v),
rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()),
col=c("black","darkred")[1+
((rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))>input$beta0)+((rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))<input$beta0)
])
})
output$beta0ictesto=renderText({
req(length(rv$beta0.v)>0)
paste(sum(((rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))>input$beta0)+((rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))<input$beta0)),
"of",
length(rv$beta1.v),"(",
round(100*sum(((rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))>input$beta0)+((rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))<input$beta0))/length(rv$beta1.v),1),"%)")
})
output$beta1ic=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
plot(rv$beta1.v,1:length(rv$beta1.v),
bty="n",
yaxt="n",
xaxt="n",
xlim=c(input$beta1-2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx()),
input$beta1+2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx())),
ylim=c(0,max(100,length(rv$beta1.v))),
xlab=expression(hat(beta)[2]))
axis(1,at=signif(c(input$beta1-4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx()),
input$beta1+c(-1,1,-0.5,0.5)*2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx()),
input$beta1,
input$beta1+4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx())),2))
abline(v=input$beta1,col=gray(0.8),lwd=2)
segments(rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()),
1:length(rv$beta1.v),
rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()),
col=c("black","darkred")[1+
((rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))>input$beta1)+((rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))<input$beta1)
])
})
output$beta1ictesto=renderText({
req(length(rv$beta0.v)>0)
paste(sum(((rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))>input$beta1)+((rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))<input$beta1)),
"of",
length(rv$beta1.v),"(",
round(100*sum(((rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))>input$beta1)+((rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))<input$beta1))/length(rv$beta1.v),1),"%)")}
)
output$residui1=renderPlot({
par(mar=c(5,4,1,1))
plot(x(),fit()$resid,pch=20,las=1,
xlab="x",ylab="residuals")
abline(h=0)
})
output$residui2=renderPlot({
par(mar=c(5,3,1,1))
hist(fit()$resid,border="white",col=gray(0.6),main="",xlab="residuals")
})
output$residui3=renderPlot({
par(mar=c(5,3,1,1))
qqnorm(fit()$resid,pch=20,main="")
qqline(fit()$resid,pch=20)
})
}
shinyApp(ui = ui, server = server)
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#library(shiny)
#library(shinyjs)
ui <- fluidPage(
shinyjs::useShinyjs(),
withMathJax(),
# tags$img(width=300,height=50,src="deams.png"),
# tags$img(width=300,height=50,src="logoUnits2.jpg"),
h1("Simple linear regression"),
#tabsetPanel(
# tabPanel("a",
# Input functions
sidebarLayout(
sidebarPanel(
sliderInput("n","Number of observations",min=8,max=1000,value=25,step=1),
hr(),
p(strong("Model: \\(y_i=\\beta_1+\\beta_2x_i+\\varepsilon_i\\), \\(\\varepsilon_i\\thicksim IID(\\mathcal N(0,\\sigma^2))\\)")),
splitLayout(
numericInput("beta0","\\(\\beta_1\\)",0,-10,10,0.1,width="100%"),
numericInput("beta1","\\(\\beta_2\\)",1,-10,10,0.1,width="100%"),
numericInput("sdeverr","\\(\\sigma\\)",1,0,10,0.1,width="100%")
),
hr(),
p(strong("Explanatory variable")),
splitLayout(
numericInput("sdevx","\\(\\sqrt{V(x)}\\)",0.5,0,1,0.1,width="100%"),
numericInput("xbar","\\(\\bar{x}\\)",0,-3,3,0.1,width="100%")
),
checkboxInput("mostra","show estimates on plot"),
hr(),
actionButton("aggiorna","Draw Y"),
p("A new sample for Y is drawn based on the input parameters."),
actionButton("aggiorna2","Draw Y repeatedly"),
p("A new simulation will be drawn every 0.5/0.1 seconds"),
hr(),
p("Sample distributions and c.i. plots are reset if any parameter is changed."),
hr(),
actionButton("scarica","Download data"),
p("Saves data in temp.csv in the working directory")
),
mainPanel(
fluidRow(
column(width = 8,{
verticalLayout(
plotOutput("scatter")
)
}),
column(width = 4,
wellPanel(
plotOutput("stim")
))
),
tabsetPanel(
tabPanel("Residuals",
splitLayout(
plotOutput("residui1", width = "100%"),
plotOutput("residui2", width = "100%"),
plotOutput("residui3", width = "100%")
)
),
tabPanel("Sample dist. coefs",
splitLayout(
plotOutput("beta0plot", width = "100%"),
plotOutput("beta1plot", width = "100%"),
plotOutput("beta0beta1", width = "100%")
),
textOutput("numsim")
),
tabPanel("Conf. int.",
splitLayout(
wellPanel(
numericInput("livconf","Confidence level",0.95,0.5,0.999,0.001,width="100%"),
p("Do not cover the true value"),
p(textOutput("beta0ictesto")),
p(textOutput("beta1ictesto"))
),
plotOutput("beta0ic", width = "100%"),
plotOutput("beta1ic", width = "100%")
)
),
tabPanel("Sample dist var",
splitLayout(
plotOutput("sigmaplot", width = "100%"),
plotOutput("sigma2plot", width = "100%")
),
textOutput("numsim2")
),
tabPanel("Piv. Q.",
splitLayout(
plotOutput("qp1plot", width = "100%"),
plotOutput("qp2plot", width = "100%")
),
textOutput("numsim3")
),
tabPanel("Prediction",
splitLayout(
wellPanel(
verticalLayout(
checkboxInput("previsioni","Show predictions on plot"),
sliderInput("livello","Level",0.5,0.99,0.90,0.01,width="100%"),
sliderInput("extra","extrapolation (%)",0,200,0,1,width="100%")
)),
plotOutput("previsioniv")
)
)
)
)
# p("Prova a inventare un insieme di osservazioni che corrisponda al diagrama a scatola disegnato sopra."),
# textInput('vec1', 'Inserisci le osservazioni separate da , (usa il . per i decimali)', ""),
# Ouptut functions
# actionButton("invio","Invia"),
# plotOutput("boxplot2", width = "66%")
)
)
# textOutput("qq1")),
nintf=function(x) {
if (length(x)<50) 5
if ((length(x)>=50) & (length(x)<500)) 20
if ((length(x)>=500)) 30
}
server <- function(input, output, session) {
# input$<id> available
# data <- reactive ({}) #respond to every value in input, to be used as data()
# output$<nomeoutput> <- render<TIPO>({ <codice> })
rv=reactiveValues()
rv$beta0.v=c()
rv$beta1.v=c()
rv$sigma.v=c()
rv$sd.v=c()
fit=reactive({fit=lm(y()~x())})
summfit=reactive({summary(fit())})
tempo=reactiveVal(30000000000000000)
observeEvent(input$aggiorna2,{
if ((input$aggiorna2 %% 3)==0){
tempo(30000000000000000)
updateActionButton(session, "aggiorna2",label="Draw Y repeatedly")
} else {
if ((input$aggiorna2 %% 3)==1){
tempo(500)
updateActionButton(session, "aggiorna2",label="Accelerate drawings")
} else {
tempo(50)
updateActionButton(session, "aggiorna2",label="Stop automatic drawings")
}
}
})
observe({
shinyjs::click("aggiorna")
invalidateLater(tempo())
})
observeEvent(y(),{
temp=rv$beta1.v
temp=c(temp,fit()$coefficients[2])
rv$beta1.v=temp
temp=rv$beta0.v
temp=c(temp,fit()$coefficients[1])
rv$beta0.v=temp
temp=rv$sigma.v
temp=c(temp,sum(fit()$resid^2)/(input$n-2))
rv$sigma.v=temp
})
observeEvent(input$n*input$beta0*input$beta1*input$sdeverr*input$sdevx*input$xbar,{
rv$beta1.v=c()
rv$beta0.v=c()
rv$sigma.v=c()
})
observeEvent(input$scarica,{
#dati=data.frame(x=x(),y=y())
#.GlobalEnv$results.SimpleLM=dati
write.table(dati,sep=",",file=paste0(.wd,"/temp.csv"))
})
output$numsim=renderText(
paste("Sample distributions of estimators based on ",
length(rv$beta1.v),
"simulations; green: true values, gray: theorical distribution, triangle: mean of simulated estimates.")
)
output$numsim2=renderText(
paste("Sample distributions of estimators based on ",
length(rv$beta1.v),
"simulations; green: true values, gray: theorical distribution.")
)
output$numsim3=renderText(
paste("Sample distributions of pivotal quantities based on",
length(rv$beta1.v),
"simulations; green: theorical distribution.")
)
output$stim=renderPlot({
req(is.numeric(input$beta1))
par(mar=c(1,1,1,1),cex=1.5)
plot(c(0,1),c(1.5,9),type="n",bty="n",xaxt="n",yaxt="n",xlab="n",ylab="n")
text(0,9,adj=c(0,1),col="darkred",
label=substitute(paste(hat(beta)[1],"=",b0),
list(b0=signif(fit()$coef[1],3),vb1=signif(summfit()$coefficients[1,2],3))))
text(0,8,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(hat(v)(hat(beta)[1])),"=",vb1),
list(b0=signif(fit()$coef[1],3),vb1=signif(summfit()$coefficients[1,2],3))))
text(0,7,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(v(hat(beta)[1])),"=",vb1v),
list(vb1v=signif(input$sdeverr*sqrt(1/input$n+input$xbar^2/Dx()),3))))
text(0,6,adj=c(0,1),col="darkred",
label=substitute(paste(hat(beta)[2],"=",b1),
list(b1=signif(fit()$coef[2],3))))
text(0,5,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(hat(v)(hat(beta)[2])),"=",vb2),
list(b1=signif(fit()$coef[1],3),vb2=signif(summfit()$coefficients[2,2],3))))
text(0,4,adj=c(0,1),col="darkred",
label=substitute(paste(sqrt(v(hat(beta)[2])),"=",vb1v),
list(vb1v=signif(input$sdeverr*sqrt(1/Dx()),3))))
text(0,3,adj=c(0,1),col="darkred",
label=substitute(paste(s^2,"=",s2," (s=",ss,")"),
list(s2=signif(summfit()$sigma^2,3),ss=signif(summfit()$sigma,3))))
text(0,2,adj=c(0,1),col="darkred",
label=substitute(paste(R^2,"=",r2),
list(r2=signif(summfit()$r.squared,3))))
})
x=eventReactive(input$n*input$sdevx*input$xbar,{
req(is.numeric(input$xbar) & is.numeric(input$sdevx) & (input$sdevx>0))
x=rnorm(input$n,0,1)
x=(x-mean(x))/sd(x)
x=input$xbar+input$sdevx*x
return(x)
})
Dx=reactive({sum((x()-input$xbar)^2)})
y=eventReactive(
input$aggiorna*input$n*input$beta0*input$beta1*input$sdeverr*input$sdevx*input$xbar, {
req(is.numeric(input$beta1) & is.numeric(input$beta0)& is.numeric(input$sdeverr) & (input$sdeverr>0))
#autoInvalidate()
y=input$beta0+input$beta1*x()+rnorm(input$n,0,input$sdeverr)
return(y)
},ignoreNULL = FALSE)
output$scatter=renderPlot({
par(mar=c(4,4,1,1))
if (input$mostra){
limx=c(min(c(0,1,x())),max(c(0,1.1,x())))
limy=range(c(input$beta0+input$beta1*(input$xbar+c(-1,1)*4*input$sdevx)+c(-1,1)*3*input$sdeverr,input$beta0+c(-1,1)*qnorm(0.95)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),input$beta0+c(-1,1,-1,1)*qnorm(0.95)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())+input$beta1+c(-1,-1,1,1)*qnorm(0.95)*input$sdeverr*sqrt(1/Dx())))
} else {
limx=c(min(x()),max(x()))
limy=range(input$beta0+input$beta1*(input$xbar+c(-1,1)*4*input$sdevx))+c(-1,1)*3*input$sdeverr
}
if (input$previsioni){
updateCheckboxInput(session, "mostra",value=FALSE)
limx=c(min(x())-(input$extra/200)*(max(x())-min(x())),max(x())+(input$extra/200)*(max(x())-min(x())))
limy=range(c(input$beta0+input$beta1*limx[1]+c(-1,1)*qt(0.99,5)*input$sdeverr*sqrt(1+1/input$n+(limx[1]-input$xbar)^2/Dx()),
input$beta0+input$beta1*limx[2]+c(-1,1)*qt(0.99,5)*input$sdeverr*sqrt(1+1/input$n+(limx[2]-input$xbar)^2/Dx())
))
}
a=plot(x(),y(),xlim=limx,
ylim=limy,las=1,xlab="x",ylab="y",las=1,pch=20,yaxt="n",bty="n")
axis(1,at=c(limx[1]-1,limx[2]+1),labels=c("",""))
axis(2,las=1,
at=c(limy[1]-4,limy[2]+4),
labels=c("",""))
axis(2,las=1,
at=c(limy,input$beta0),
labels=signif(c(limy,input$beta0),3))
rug(x())
text(ifelse(input$beta1>0,limx[1],limx[2]),limy[2],adj=c(0+(input$beta1<=0),1),col="darkred",
label=substitute(paste(hat(y),"=",b0,segno,b1,"x"," (est. reg. line)"),
list(b0=signif(fit()$coef[1],3),b1=signif(fit()$coef[2],3),r2=signif(summfit()$r.squared,3),segno=ifelse(fit()$coef[2]>0,"+","")))
)
text(ifelse(input$beta1>0,limx[1],limx[2]),limy[2]-0.1*(limy[2]-limy[1]),adj=c(0+(input$beta1<=0),1),col="darkgray",
label=substitute(paste(E(y),"=",b0,segno,b1,"x"," (true reg. line)"),
list(b0=signif(input$beta0,3),b1=signif(input$beta1,3),segno=ifelse(input$beta1>0,"+","")))
)
# expression(paste("Retta stimata:",hat(y),"=",signif(fit()$coef[1],3)," + ",signif(fit()$coef[2],3),"x")))
curve(input$beta0+input$beta1*x,col=gray(0.5),lwd=2,add=TRUE)
curve(fit()$coef[1]+fit()$coef[2]*x,col="darkred",lwd=2,add=TRUE)
if (input$mostra){
par(xpd=NA)
text(0,fit()$coef[1],adj=c(fit()$coef[2]>=0,0),
labels=expression(hat(beta)[1]),col="darkgreen",cex=1.5)
text(1,mean(c(fit()$coef[1],fit()$coef[1]+fit()$coef[2])),pos=4,labels=expression(hat(beta)[2]),col="darkgreen",cex=1.5)
par(xpd=FALSE)
points(0,fit()$coef[1],pch=20,cex=1.5,col="darkgreen")
abline(v=c(0,1),lty=2)
segments(1,fit()$coef[1],1,fit()$coef[1]+fit()$coef[2],lwd=2,col="darkgreen")
segments(0,fit()$coef[1],1,fit()$coef[1],lty=2)
}
if (input$previsioni){
xseq=seq(limx[1],limx[2],length=100)
polygon(c(xseq,rev(xseq)),c(fit()$coef[1]+fit()$coef[2]*xseq+qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1/input$n+(xseq-input$xbar)^2/Dx()),fit()$coef[1]+fit()$coef[2]*rev(xseq)-qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1/input$n+(rev(xseq)-input$xbar)^2/Dx())),border=NA,col="#8C000069")
curve(fit()$coef[1]+fit()$coef[2]*x+qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1+1/input$n+(x-input$xbar)^2/Dx()),add=TRUE,lwd=2,col="darkred",lty=3)
curve(fit()$coef[1]+fit()$coef[2]*x-qt((1-input$livello)/2,input$n-2)*summfit()$sigma*sqrt(1+1/input$n+(x-input$xbar)^2/Dx()),add=TRUE,lwd=2,col="darkred",lty=3)
}
})
output$beta1plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(rv$beta1.v,n=nintf(rv$beta1.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(beta)[2]),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dnorm(input$beta1,input$beta1,input$sdeverr*sqrt(1/Dx())))))
points(input$beta1,0,pch=20,col="darkgreen",cex=3)
points(mean(rv$beta1.v),0,pch=17,col="black",cex=2.2)
curve(dnorm(x,input$beta1,input$sdeverr*sqrt(1/Dx())),add=TRUE,col=gray(0.7),lwd=2)
})
output$beta0plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(rv$beta0.v,n=nintf(rv$beta0.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(beta)[1]),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dnorm(input$beta0,input$beta0,input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())))))
points(input$beta0,0,pch=20,col="darkgreen",cex=3)
points(mean(rv$beta0.v),0,pch=17,col="black",cex=2.2)
curve(dnorm(x,input$beta0,input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())),add=TRUE,col=gray(0.7),lwd=2)
})
output$qp1plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
qp=(rv$beta0.v-input$beta0)/(rv$sigma.v*sqrt(1/input$n+input$xbar^2/Dx()))
a= hist(qp,n=nintf(qp))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(t[1]),freq=FALSE,
xlim=range(c(qt(c(0.001,0.999),df=input$n-2),qp)),ylim=c(0,max(1.2*dt(0,df=input$n-2),0*a$density)))
curve(dt(x,df=input$n-2),add=TRUE,col="darkgreen",lwd=2)
})
output$qp2plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
qp=(rv$beta1.v-input$beta1)/(rv$sigma.v*sqrt(1/Dx()))
a= hist(qp,n=nintf(qp))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(t[2]),freq=FALSE,
xlim=range(c(qt(c(0.001,0.999),df=input$n-2),qp)),ylim=c(0,max(1.2*dt(0,df=input$n-2),0*a$density)))
curve(dt(x,df=input$n-2),add=TRUE,col="darkgreen",lwd=2)
})
output$beta0beta1=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,5,1,1))
plot(rv$beta0.v,rv$beta1.v,pch=20,col="darkred",xlab=expression(hat(beta)[1]),ylab=expression(hat(beta)[2]),las=1)
points(input$beta0,input$beta1,pch=20,col="darkgreen",cex=2)
})
output$previsioniv=renderPlot({
par(mar=c(5,4,0.5,0.5))
limx=c(min(x()),max(x()))
if (input$previsioni){
limx=c(min(x())-(input$extra/200)*(max(x())-min(x())),max(x())+(input$extra/200)*(max(x())-min(x())))
}
matplot(matrix(rep(limx,length(rv$beta0.v)),nrow=2),
rbind(rv$beta0.v+rv$beta1.v*limx[1],rv$beta0.v+rv$beta1.v*limx[2]),type="l",lty=1,col="#8C000069",
xlab="x",ylab="y")
abline(c(input$beta0,input$beta1),col=gray(0.25),lwd=2)
})
output$sigmaplot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(sqrt(rv$sigma.v),n=nintf(rv$sigma.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(sigma)),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dchisq(input$n-2,input$n-2)*2*sqrt(input$sdeverr^2)*(input$n-2)/input$sdeverr^2)))
points(input$sdeverr,0,pch=20,col="darkgreen",cex=3)
curve(dchisq(x^2*(input$n-2)/input$sdeverr^2,input$n-2)*2*x*(input$n-2)/input$sdeverr^2,col=gray(0.7),lwd=2,add=TRUE)
})
output$sigma2plot=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
a=hist(rv$sigma.v,n=nintf(rv$sigma.v))
plot(a,main="",yaxt="n",border="white",col="darkred",xlab=expression(hat(sigma)^2),freq=FALSE,
ylim=c(0,max(0*a$density,1.2*dchisq(input$n-2,input$n-2)*(input$n-2)/input$sdeverr^2)))
points(input$sdeverr^2,0,pch=20,col="darkgreen",cex=3)
curve(dchisq(x*(input$n-2)/input$sdeverr^2,input$n-2)*(input$n-2)/input$sdeverr^2,col=gray(0.7),lwd=2,add=TRUE)
})
output$beta0ic=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
plot(rv$beta0.v,1:length(rv$beta1.v),
bty="n",
yaxt="n",
xaxt="n",
xlim=c(input$beta0-2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),
input$beta0+2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())),
ylim=c(0,max(100,length(rv$beta1.v))),
xlab=expression(hat(beta)[1]))
axis(1,at=signif(c(input$beta0-4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),
input$beta0+c(-1,1,-0.5,0.5)*2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx()),
input$beta0,
input$beta0+4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/input$n+mean(x())^2/Dx())),2))
abline(v=input$beta0,col=gray(0.8),lwd=2)
segments(rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()),
1:length(rv$beta0.v),
rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()),
col=c("black","darkred")[1+
((rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))>input$beta0)+((rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))<input$beta0)
])
})
output$beta0ictesto=renderText({
req(length(rv$beta0.v)>0)
paste(sum(((rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))>input$beta0)+((rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))<input$beta0)),
"of",
length(rv$beta1.v),"(",
round(100*sum(((rv$beta0.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))>input$beta0)+((rv$beta0.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/input$n+mean(x())^2/Dx()))<input$beta0))/length(rv$beta1.v),1),"%)")
})
output$beta1ic=renderPlot({
req(length(rv$beta0.v)>0)
par(mar=c(5,1,1,1))
plot(rv$beta1.v,1:length(rv$beta1.v),
bty="n",
yaxt="n",
xaxt="n",
xlim=c(input$beta1-2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx()),
input$beta1+2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx())),
ylim=c(0,max(100,length(rv$beta1.v))),
xlab=expression(hat(beta)[2]))
axis(1,at=signif(c(input$beta1-4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx()),
input$beta1+c(-1,1,-0.5,0.5)*2*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx()),
input$beta1,
input$beta1+4*qnorm(1-(1-input$livconf)/5)*input$sdeverr*sqrt(1/Dx())),2))
abline(v=input$beta1,col=gray(0.8),lwd=2)
segments(rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()),
1:length(rv$beta1.v),
rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()),
col=c("black","darkred")[1+
((rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))>input$beta1)+((rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))<input$beta1)
])
})
output$beta1ictesto=renderText({
req(length(rv$beta0.v)>0)
paste(sum(((rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))>input$beta1)+((rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))<input$beta1)),
"of",
length(rv$beta1.v),"(",
round(100*sum(((rv$beta1.v-qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))>input$beta1)+((rv$beta1.v+qt(1-(1-input$livconf)/2,input$n-2)*sqrt(rv$sigma.v)*sqrt(1/Dx()))<input$beta1))/length(rv$beta1.v),1),"%)")}
)
output$residui1=renderPlot({
par(mar=c(5,4,1,1))
plot(x(),fit()$resid,pch=20,las=1,
xlab="x",ylab="residuals")
abline(h=0)
})
output$residui2=renderPlot({
par(mar=c(5,3,1,1))
hist(fit()$resid,border="white",col=gray(0.6),main="",xlab="residuals")
})
output$residui3=renderPlot({
par(mar=c(5,3,1,1))
qqnorm(fit()$resid,pch=20,main="")
qqline(fit()$resid,pch=20)
})
}
shinyApp(ui = ui, server = server)
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