Latihan Pertemuan 6 PML

Nomor 1

a

x1<- matrix(c(12,14,16,18,20,22),,1)
x <- cbind(1,x1)
y <- matrix(c(2.5,3,3.5,4.5,5,5.5),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##            [,1]
## [1,] -1.3428571
## [2,]  0.3142857

b

model <- lm(y~x1)
confint(model,level=0.95)
##                 2.5 %     97.5 %
## (Intercept) -2.185181 -0.5005329
## x1           0.265708  0.3628634

Nomor 2

a

x2<- matrix(c(100,150,200,250,300),,1)
x <- cbind(1,x2)
y <- matrix(c(3.2,4.1,5,5.8,6.5),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##        [,1]
## [1,] 1.6000
## [2,] 0.0166

b

model <- lm(y~x2)
confint(model,level=0.95)
##                 2.5 %    97.5 %
## (Intercept) 1.2602077 1.9397923
## x2          0.0149982 0.0182018

Nomor 3

a

x3<- matrix(c(5,10,15,20,25,30),,1)
x <- cbind(1,x3)
y <- matrix(c(20,25,30,35,40,45),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##      [,1]
## [1,]   15
## [2,]    1

b

model <- lm(y~x3)
confint(model,level=0.95)
## Warning in summary.lm(object, ...): essentially perfect fit: summary may be
## unreliable
##             2.5 % 97.5 %
## (Intercept)    15     15
## x3              1      1

Nomor 4

a

x4<- matrix(c(20,25,30,35,40,45,50),,1)
x <- cbind(1,x4)
y <- matrix(c(1.5,2,2.5,3,3.5,4,4.5),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##      [,1]
## [1,] -0.5
## [2,]  0.1

b

model <- lm(y~x4)
confint(model,level=0.95)
## Warning in summary.lm(object, ...): essentially perfect fit: summary may be
## unreliable
##             2.5 % 97.5 %
## (Intercept)  -0.5   -0.5
## x4            0.1    0.1

Nomor 5

a

x5<- matrix(c(3:8),,1)
x <- cbind(1,x5)
y <- matrix(c(10,12,15,18,20,22),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##          [,1]
## [1,] 2.495238
## [2,] 2.485714

b

model <- lm(y~x5)
confint(model,level=0.95)
##                 2.5 %   97.5 %
## (Intercept) 0.8908398 4.099636
## x5          2.2071270 2.764302

Nomor 6

a

x6<- matrix(c(50,75,100,125,150,175),,1)
x <- cbind(1,x6)
y <- matrix(c(4.5,5,5.5,6,6.5,7),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##      [,1]
## [1,] 3.50
## [2,] 0.02

b

model <- lm(y~x6)
confint(model,level=0.95)
## Warning in summary.lm(object, ...): essentially perfect fit: summary may be
## unreliable
##             2.5 % 97.5 %
## (Intercept)  3.50   3.50
## x6           0.02   0.02

Nomor 7

a

x7<- matrix(c(200,250,300,350,400),,1)
x <- cbind(1,x7)
y <- matrix(c(150,175,200,225,250),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##      [,1]
## [1,] 50.0
## [2,]  0.5

b

model <- lm(y~x7)
confint(model,level=0.95)
## Warning in summary.lm(object, ...): essentially perfect fit: summary may be
## unreliable
##             2.5 % 97.5 %
## (Intercept)  50.0   50.0
## x7            0.5    0.5

Nomor 8

a

x8<- matrix(c(5,10,15,20,25,30),,1)
x <- cbind(1,x8)
y <- matrix(c(60,70,75,85,90,95),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##          [,1]
## [1,] 54.66667
## [2,]  1.40000

b

model <- lm(y~x8)
confint(model,level=0.95)
##                 2.5 %    97.5 %
## (Intercept) 49.947617 59.385716
## x8           1.157652  1.642348

Nomor 9

a

x9<- matrix(c(50,100,150,200,250),,1)
x <- cbind(1,x9)
y <- matrix(c(1.5,2,2.5,3,3.5),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##      [,1]
## [1,] 1.00
## [2,] 0.01

b

model <- lm(y~x9)
confint(model,level=0.95)
## Warning in summary.lm(object, ...): essentially perfect fit: summary may be
## unreliable
##             2.5 % 97.5 %
## (Intercept)  1.00   1.00
## x9           0.01   0.01

Nomor 10

a

x10<- matrix(c(100,150,200,250,300,350),,1)
x <- cbind(1,x10)
y <- matrix(c(2,2.5,3,3.5,4,4.5),,1)
xtx <- t(x)%*%x
xtxinv <- solve(xtx)
xty <- t(x)%*%y
b <- xtxinv%*%xty
b
##      [,1]
## [1,] 1.00
## [2,] 0.01

b

model <- lm(y~x10)
confint(model,level=0.95)
## Warning in summary.lm(object, ...): essentially perfect fit: summary may be
## unreliable
##             2.5 % 97.5 %
## (Intercept)  1.00   1.00
## x10          0.01   0.01