DD<-matrix(c(
  26.2,110,
  33,89,
  17.5,102,
  25.25,98,
  20.3,110,
  31.9,98,
  21.1,122,
  22.7,119,
  10.7,120,
  22.1,92
),10,2,byrow=T)
DD<-matrix(c(
  26.2,110,
  33,89,
  17.5,102,
  25.25,98,
  20.3,110,
  31.9,98,
  21.1,122,
  22.7,119,
  10.7,120,
  22.1,92
),10,2,byrow=T)
DD<-as.data.frame(DD)
names(DD)<-c("IC","QI")
ld<-lm(IC~QI,DD)
summary(ld)
#alternativa
y<-c(26.20 ,33.00 ,17.50 ,25.25,20.30 ,31.90, 21.10, 22.70 ,10.70 ,22.10)
x<-c(110, 89, 102 , 98, 110,  98, 122, 119, 120,  92)

l<-lm(y~x)
summary(l)
confint(l,level=0.99)
pl<-predict(l,level=0.99,
            interval="confidence")
cbind(x,y,pl)
n<-length(y)
mx<-mean(x)
mx
my<-mean(y)
my
vy<-var(y)*(n-1)/n
vy
vx<-var(x)*(n-1)/n
vx
mxy<-mean(x*y)
mxy
vxy<-mean(x*y)-mx*my
vxy
#stima intercetta e coeff. angolare
b<-vxy/vx
b
a<-my-b*mx
a
#calcolo var residua
r2<-vxy^2/vx/vy
r2
stilde<-vy*(1-r2)*n/(n-2)
#intervalli confidenza per valore atteso y dato x=100,lc=0.9
y_100<-a+b*100
v_100<-stilde*(1/n+(100-mx)^2/n/vx)
perc<-qt(0.95,n-2)
IC<-c(y_100-perc*sqrt(v_100),y_100+perc*sqrt(v_100))
IC
#intervallo previsivo
y_100<-a+b*100
perc<-qt(0.95,n-2)
v_100pre<-stilde*(1+1/n+(100-mx)^2/(n*vx))
IPRE<-c(y_100-perc*sqrt(v_100pre),y_100+perc*sqrt(v_100pre))
IPRE

#confint b lc=0.99
vb<-stilde/n/vx
sqrt(vb)
perc<-qt(0.995,n-2)
IC<-c(b-perc*sqrt(vb),b+perc*sqrt(vb))
IC

#test hp e pvalue H_0:beta10=-0.1 alpha=0.05 DX
vb<-stilde/n/vx

bnull<--0.1
test<-(b-bnull)/sqrt(vb)
test
perc<-qt(0.95,n-2)
perc
pvaldx<-1-pt(test,n-2)
pvaldx
#test hp e pvalue H_0:b10= 0.1 alpha=0.05 alt sx
bnull=0.1
test<-(b-bnull)/sqrt(vb)
test
perc<-qt(0.05,n-2)
pvalsx<-pt(test,n-2)
pvalsx

# alpha 0.01 H_0 bl0=0.1 bilat
bnull=0.1
test<-(b-bnull)/sqrt(vb)
test

pvalbil<-2*(1-pt(abs(test),n-2))
pvalbil