##READ DATA

data <- read.csv("C:\\Users\\HESTY\\Desktop\\SEMESTER 4\\Analisis Regresi\\Praktikum\\data liver.csv", sep=";")


y<-data$Y
x2<-data$X2

data<-data.frame(cbind(y,x2))
head(data)
##        y    x2
## 1 158.76  8.90
## 2 197.19 21.22
## 3 144.73 16.62
## 4 140.06 22.86
## 5 129.71 14.23
## 6 162.59 17.35
n<-nrow(data)
n
## [1] 36
p<-ncol(data)
p
## [1] 2

##EKSPLORASI DATA

plot(x2,y)

summary(y)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   120.9   143.9   160.7   169.7   191.8   247.4
boxplot(y)

summary(x2)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.270   6.335   9.220  11.549  15.207  36.360

##PEMBENTUKAN 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)
b1
## [1] 2.243073
b0
## [1] 143.8205

#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
r
## [1] 0.509127
Adj_R2<-1-((1-Koef_det)*(n-1)/(n-1-1))
Adj_R2
## [1] 0.2374224
Adj_R2
## [1] 0.2374224

#STD. 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

##SIGNIFIKASI 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