Menginput Data & Package

#Data
data = read.table(file.choose(), header=T)
data
##      Y  X1   X2   X3
## 1 57.5  78 2.75 29.5
## 2 52.8  69 2.15 26.3
## 3 61.3  77 4.41 32.2
## 4 67.0  88 5.52 36.5
## 5 53.5  67 3.21 27.2
## 6 62.7  80 4.32 27.7
## 7 56.2  74 2.31 28.3
## 8 68.5  94 4.30 30.3
## 9 69.2 102 3.71 28.7
#Package
library(ggplot2)
library(car)
## Loading required package: carData
library(lmtest)
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(zoo)

Scatter Plot

X1 & Y

ggplot(data, aes(x = X1, y = Y, group = 1)) +
  geom_point(color = "pink", size = 3) +
  geom_smooth(method = "lm", colour = "maroon", linewidth = 1) +
  labs(title = "Scatter Plot X1 & Y", x = "X1", y = "Y") +
  theme_minimal(base_size = 13) +
  theme(
    plot.title = element_text(face = "bold", hjust = 0.5),
    axis.title = element_text(face = "bold")
  )
## `geom_smooth()` using formula = 'y ~ x'

X2 & Y

ggplot(data, aes(x = X2, y = Y, group = 1)) +
  geom_point(color = "pink", size = 3) +
  geom_smooth(method = "lm", colour = "maroon", linewidth = 1) +
  labs(title = "Scatter Plot X2 & Y", x = "X2", y = "Y") +
  theme_minimal(base_size = 13) +
  theme(
    plot.title = element_text(face = "bold", hjust = 0.5),
    axis.title = element_text(face = "bold")
  )
## `geom_smooth()` using formula = 'y ~ x'

X3 & Y

ggplot(data, aes(x = X3, y = Y, group = 1)) +
  geom_point(color = "pink", size = 3) +
  geom_smooth(method = "lm", colour = "maroon", linewidth = 1) +
  labs(title = "Scatter Plot X3 & Y", x = "X3", y = "Y") +
  theme_minimal(base_size = 13) +
  theme(
    plot.title = element_text(face = "bold", hjust = 0.5),
    axis.title = element_text(face = "bold")
  )
## `geom_smooth()` using formula = 'y ~ x'

Model Regresi

reg=lm(Y~X1+X2+X3, data=data)
summary(reg)
## 
## Call:
## lm(formula = Y ~ X1 + X2 + X3, data = data)
## 
## Residuals:
##       1       2       3       4       5       6       7       8       9 
## -0.2981 -0.2142  0.4714 -0.4746 -0.9524  0.4761  0.9274  0.7466 -0.6823 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 21.87353    4.07389   5.369  0.00302 ** 
## X1           0.41277    0.03067  13.460 4.05e-05 ***
## X2           2.20267    0.47199   4.667  0.00550 ** 
## X3          -0.07895    0.15551  -0.508  0.63330    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8484 on 5 degrees of freedom
## Multiple R-squared:  0.9888, Adjusted R-squared:  0.9821 
## F-statistic: 147.1 on 3 and 5 DF,  p-value: 2.696e-05

Uji Asumsi Klasik

Pendeteksian Multikolinieritas (< 10)

vif(reg)
##       X1       X2       X3 
## 1.403219 3.093549 2.607991

Uji Non-Heteroskedastisitas

#Breusch-Pagan Test
bptest(reg)
## 
##  studentized Breusch-Pagan test
## 
## data:  reg
## BP = 0.52402, df = 3, p-value = 0.9136
#Glejser Test
res=resid(reg)
res
##          1          2          3          4          5          6          7 
## -0.2980857 -0.2141744  0.4714083 -0.4745650 -0.9524106  0.4760829  0.9274363 
##          8          9 
##  0.7466056 -0.6822975
ae=abs(res)
ae
##         1         2         3         4         5         6         7         8 
## 0.2980857 0.2141744 0.4714083 0.4745650 0.9524106 0.4760829 0.9274363 0.7466056 
##         9 
## 0.6822975
regm=lm(formula = ae~X1+X2+X3, data=data)
summary(regm)
## 
## Call:
## lm(formula = ae ~ X1 + X2 + X3, data = data)
## 
## Residuals:
##        1        2        3        4        5        6        7        8 
## -0.24968 -0.37078 -0.06495 -0.01987  0.35744 -0.17650  0.37477  0.12608 
##        9 
##  0.02347 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  1.000238   1.548904   0.646    0.547
## X1           0.002391   0.011660   0.205    0.846
## X2           0.035130   0.179452   0.196    0.853
## X3          -0.024936   0.059127  -0.422    0.691
## 
## Residual standard error: 0.3226 on 5 degrees of freedom
## Multiple R-squared:  0.04467,    Adjusted R-squared:  -0.5285 
## F-statistic: 0.07793 on 3 and 5 DF,  p-value: 0.9692

Uji Non-Autokorelasi

#Breusch-Godfrey test
bgtest(reg)
## 
##  Breusch-Godfrey test for serial correlation of order up to 1
## 
## data:  reg
## LM test = 0.51249, df = 1, p-value = 0.4741
#Durbin-Watson Test
dwtest(reg)
## 
##  Durbin-Watson test
## 
## data:  reg
## DW = 1.6446, p-value = 0.1165
## alternative hypothesis: true autocorrelation is greater than 0

Uji Normalitas

Jika sampel < 30 menggunakan shapiro-wilk, namun jika sampel > 30 menggunakan lilliefors

#Shapiro-Wilk Test
shapiro.test(resid(reg))
## 
##  Shapiro-Wilk normality test
## 
## data:  resid(reg)
## W = 0.93208, p-value = 0.5014