Membaca data

data <- read.csv("C:/Users/keyzh/OneDrive/Desktop/OneDrive/Documents/keke/SEMESTER 4/Analisis Regresi/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<-data.frame(cbind(y,x1,x2,x3,x4,x5,x6))
head(data)
##        y    x1    x2   x3    x4    x5   x6
## 1 158.76 16.36  8.90 3.47  6.02 57.42 1.11
## 2 197.19 26.68 21.22 3.53 12.07 61.38 1.36
## 3 144.73 12.49 16.62 2.00  8.88 67.42 1.47
## 4 140.06  8.45 22.86 6.71  7.46 69.94 1.31
## 5 129.71 10.19 14.23 4.75  2.06 65.68 1.25
## 6 162.59 19.53 17.35 1.95  7.54 59.63 1.14
View(data)

n<-nrow(data)
n
## [1] 36
p<-ncol(data)
p
## [1] 7

Explorasi Data

plot(x4,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(x4)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.060   4.065   6.095   6.811   8.998  15.000

Pembentukan Data Manual

# Parameter Regresi
b1<-(sum(x4*y)-sum(x4)*sum(y)/n)/(sum(x4^2)-(sum(x4)^2/n))
b1
## [1] 5.812239
b0<-mean(y)-b1*mean(x4)
b0
## [1] 130.1367
# Koefisien determinasi
r<-(sum(x4*y)-sum(x4)*sum(y)/n)/
  sqrt((sum(x4^2)-(sum(x4)^2/n))*(sum(y^2)-(sum(y)^2/n)))
r
## [1] 0.5636914
Koef_det<-r^2
Koef_det
## [1] 0.317748
Adj_R2<-1-((1-Koef_det)*(n-1)/(n-1-1))
Adj_R2
## [1] 0.2976818
# Std. Error
galat<-y-(b0+b1*x4)
galat
##  [1]  -6.3663695  -3.1004176 -37.0193740 -33.4359941 -12.3999016 -11.3709733
##  [7]  19.9795834 -30.6838518  -8.2948264 -31.3706397  21.9142706  39.9951881
## [13]   5.8702642  14.1416976  -8.2144919  45.9653830   0.2462733 -10.1352842
## [19]  -4.3311265  35.6773712  -0.8699714 -44.6300830  -4.8502498  63.6965934
## [25] -15.4463423  12.7859950  -8.9525861  -4.7673849 -21.2033513  20.8997211
## [31]  -8.1653259  57.1566341 -35.8996242  39.0185399  -2.1147140 -33.7246315
ragam_galat<-sum(galat^2)/(n-2)
ragam_galat
## [1] 760.4568
se_b1<-sqrt(ragam_galat/sum((x4-mean(x1))^2))
se_b1
## [1] 0.5423426
se_b0<-sqrt(ragam_galat*(1/n+mean(x4)^2/sum((x4-mean(x4))^2)))
se_b0
## [1] 10.95912
# Nilai t
t_b0<-b0/se_b0
t_b0
## [1] 11.87473
t_b1<-b1/se_b1
t_b1
## [1] 10.71692
2*pt(-abs(t_b0 ),df<-n-2)
## [1] 1.202686e-13
2*pt(-abs(t_b1 ),df<-n-2)
## [1] 1.923577e-12
# Ukuran Keragaman
galat<-y-(b0+b1*x4)
galat
##  [1]  -6.3663695  -3.1004176 -37.0193740 -33.4359941 -12.3999016 -11.3709733
##  [7]  19.9795834 -30.6838518  -8.2948264 -31.3706397  21.9142706  39.9951881
## [13]   5.8702642  14.1416976  -8.2144919  45.9653830   0.2462733 -10.1352842
## [19]  -4.3311265  35.6773712  -0.8699714 -44.6300830  -4.8502498  63.6965934
## [25] -15.4463423  12.7859950  -8.9525861  -4.7673849 -21.2033513  20.8997211
## [31]  -8.1653259  57.1566341 -35.8996242  39.0185399  -2.1147140 -33.7246315
JKG <- sum((y - (b0+b1*x4))^2)
JKG
## [1] 25855.53
JKReg <- sum(((b0+b1*x4)- mean(y))^2)
JKReg
## [1] 12041.8
JKT <- sum((y - mean(y))^2)
JKT
## [1] 37897.33
JKT <- JKReg+JKG
JKT
## [1] 37897.33
dbReg<-1
dbReg
## [1] 1
dbg<-n-2
dbg
## [1] 34
dbt<-n-1
dbt
## [1] 35
# F hitung
Fhit<-(JKReg/dbReg)/(JKG/dbg)
Fhit
## [1] 15.83496
# P Value
P.value <- 1-pf(Fhit, dbReg, dbg, lower.tail <- F)
P.value
## [1] 0.0003435874
# Pembentukan model dengan fungsi lm
model<-lm(y~x4,data<-data)
model
## 
## Call:
## lm(formula = y ~ x4, data = data <- data)
## 
## Coefficients:
## (Intercept)           x4  
##     130.137        5.812
summary(model)
## 
## Call:
## lm(formula = y ~ x4, data = data <- data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -44.630 -13.162  -4.809  15.601  63.697 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  130.137     10.959  11.875  1.2e-13 ***
## x4             5.812      1.461   3.979 0.000344 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.58 on 34 degrees of freedom
## Multiple R-squared:  0.3177, Adjusted R-squared:  0.2977 
## F-statistic: 15.83 on 1 and 34 DF,  p-value: 0.0003436
anova(model)
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x4         1  12042 12041.8  15.835 0.0003436 ***
## Residuals 34  25856   760.5                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

INTERPRETASI

Maka, dugaan persamaan garis regresi yang dihasilkan adalah ลท = 130.1367+5.812239x

Intercept (b0 = 130.1367) adalah nilai y yang diestimasi ketika x sama dengan 0.

Slope (b1 = 5.812239) adalah tingkat perubahan dalam y untuk setiap satuan perubahan dalam x. Artinya, setiap peningkatan satu satuan dalam x, kita dapat mengharapkan peningkatan sekitar 5.812239 satuan dalam y.