Read Data
data <-read.csv("C:/Users/acer/Downloads/data liver.csv",sep=";")
y<-data$Y
x1<-data$X1
x2<-data$X2
x3<-data$X3
x4<-data$X4
x5<-data$X5
x6<-data$X6
data.liver<-data.frame(cbind(y,x1,x2,x3,x4,x5,x6))
head(data)
## No X1 X2 X3 X4 X5 X6 Y
## 1 1 16.36 8.90 3.47 6.02 57.42 1.11 158.76
## 2 2 26.68 21.22 3.53 12.07 61.38 1.36 197.19
## 3 3 12.49 16.62 2.00 8.88 67.42 1.47 144.73
## 4 4 8.45 22.86 6.71 7.46 69.94 1.31 140.06
## 5 5 10.19 14.23 4.75 2.06 65.68 1.25 129.71
## 6 6 19.53 17.35 1.95 7.54 59.63 1.14 162.59
n<-nrow(data)
n
## [1] 36
p<-ncol(data)
p
## [1] 8
Pembuatan Model Tanpa Fungsi Bawaan (Manual)
Parameter Regresi
b1<-(sum(x2*y)-sum(x2)*sum(y)/n)/(sum(x2^2)-(sum(x2)^2/n))
b0<-mean(y)-b1*mean(x2)
Koefisien Determinasi dan Penyesuaiannya
r<-(sum(x2*y)-sum(x2)*sum(y)/n)/
sqrt((sum(x2^2)-(sum(x2)^2/n))*(sum(y^2)-(sum(y)^2/n)))
Koef_det<-r^2
Koef_det
## [1] 0.2592103
Adj_R2<-1-((1-Koef_det)*(n-1)/(n-1-1))
Adj_R2
## [1] 0.2374224
Standard Error Parameter Regresi
galat<-y-(b0+b1*x2)
ragam_galat<-sum(galat^2)/(n-2)
se_b1<-sqrt(ragam_galat/sum((x2-mean(x2))^2))
se_b1
## [1] 0.6503173
se_b0<-sqrt(ragam_galat*(1/n+mean(x2)^2/sum((x2-mean(x2))^2)))
se_b0
## [1] 8.90762
Signifikan Parameter (nilai-t)
t_b0<-b0/se_b0
t_b0
## [1] 16.14578
t_b1<-b1/se_b1
t_b1
## [1] 3.449198
2*pt(-abs(t_b0 ),df<-n-2)
## [1] 1.637163e-17
2*pt(-abs(t_b1 ),df<-n-2)
## [1] 0.001518399
Ukuran Keragaman
galat<-y-(b0+b1*x2)
JKG <- sum((y - (b0+b1*x2))^2)
JKReg <- sum(((b0+b1*x2)- mean(y))^2)
JKT <- sum((y - mean(y))^2)
JKT <- JKReg+JKG
dbReg<-1
dbg<-n-2
dbt<-n-1
Fhit<-(JKReg/dbReg)/(JKG/dbg)
Fhit
## [1] 11.89697
P.value<-1-pf(Fhit, dbReg, dbg, lower.tail <- F)
P.value
## [1] 0.001518399
Pembentukan Model dengan Fungsi lm
model<-lm(y~x2,data<-data)
summary(model)
##
## Call:
## lm(formula = y ~ x2, data = data <- data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -55.04 -14.52 -1.00 12.24 65.49
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 143.8205 8.9076 16.146 < 2e-16 ***
## x2 2.2431 0.6503 3.449 0.00152 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28.74 on 34 degrees of freedom
## Multiple R-squared: 0.2592, Adjusted R-squared: 0.2374
## F-statistic: 11.9 on 1 and 34 DF, p-value: 0.001518
anova(model)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x2 1 9823.4 9823.4 11.897 0.001518 **
## Residuals 34 28074.0 825.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1