Analisis Regresi Linear Berganda terhadap Faktor-Faktor yang mempengaruhi performa pembelajaran

Pendahuluan

Penelitian ini bertujuan untuk menganalisis faktor-faktor yang performa pembelajaran siswa

##IMPORT DATA

## # A tibble: 6 × 4
##   Exam_Score Hours_Studied Attendance Sleep_Hours
##        <dbl>         <dbl>      <dbl>       <dbl>
## 1         67            23         84           7
## 2         61            19         64           8
## 3         74            24         98           7
## 4         71            29         89           8
## 5         70            19         92           6
## 6         71            19         88           8

Deskripsi Data

##    Exam_Score     Hours_Studied     Attendance      Sleep_Hours    
##  Min.   : 60.00   Min.   : 4.00   Min.   : 60.00   Min.   : 4.000  
##  1st Qu.: 64.50   1st Qu.:16.00   1st Qu.: 69.00   1st Qu.: 6.000  
##  Median : 67.00   Median :19.00   Median : 78.00   Median : 7.000  
##  Mean   : 67.18   Mean   :19.39   Mean   : 79.47   Mean   : 6.768  
##  3rd Qu.: 69.00   3rd Qu.:22.50   3rd Qu.: 89.00   3rd Qu.: 8.000  
##  Max.   :100.00   Max.   :31.00   Max.   :100.00   Max.   :10.000

Penjelasan Variabel

Hourse_studied diambil berdasarakan jumlah jam belajar per minggu Attendace diambil berdasarkan persentase kehadiran dalam kelas Sleep_Hourse diambil dari rata-rata jumlah jam tidur per malam

MASUKAN MODEL REGRESI

\[ y=\beta_0+\beta_1X1+\beta_2X2+\beta_3X3+\epsilon \]

Estimasi parameter

## 
## Call:
## lm(formula = Exam_Score ~ Hours_Studied + Attendance + Sleep_Hours, 
##     data = Performa_pembelajaran)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.5060 -1.5100 -0.1057  1.0443 29.5947 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   49.64072    3.68035  13.488  < 2e-16 ***
## Hours_Studied  0.19651    0.06845   2.871  0.00505 ** 
## Attendance     0.21682    0.03060   7.087  2.4e-10 ***
## Sleep_Hours   -0.51744    0.27059  -1.912  0.05886 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.607 on 95 degrees of freedom
## Multiple R-squared:  0.3985, Adjusted R-squared:  0.3795 
## F-statistic: 20.98 on 3 and 95 DF,  p-value: 1.634e-10

##Uji Asumsi Kelasik ###Uji Normalitas Residual

error<- model1$residuals
ks.test(error,"pnorm",mean(error),sqrt(var(error)))
## 
##  Exact one-sample Kolmogorov-Smirnov test
## 
## data:  error
## D = 0.20448, p-value = 0.0004166
## alternative hypothesis: two-sided

###Uji Autokorelasi

library(lmtest)
dwtest(model1)
## 
##  Durbin-Watson test
## 
## data:  model1
## DW = 2.2921, p-value = 0.9234
## alternative hypothesis: true autocorrelation is greater than 0
library(car)
vif(model1)
## Hours_Studied    Attendance   Sleep_Hours 
##      1.053037      1.016271      1.044964
library(lmtest)
bptest(model1)
## 
##  studentized Breusch-Pagan test
## 
## data:  model1
## BP = 5.7397, df = 3, p-value = 0.125

#Scatterplot

plot(Performa_pembelajaran$Hours_Studied,
     Performa_pembelajaran$Exam_Score,
     main="Scatterplot Jam Belajar vs Nilai Ujian",
     xlab="Hours Studied",
     ylab="Exam Score",
     pch=19,
     col="steelblue")

abline(lm(Exam_Score ~ Hours_Studied,
          data = Performa_pembelajaran), col="red")

plot(Performa_pembelajaran$Attendance,
     Performa_pembelajaran$Exam_Score,
     main="Scatterplot Kehadiran vs Nilai Ujian",
     xlab="Attendance",
     ylab="Exam Score",
     pch=19,
     col="darkgreen")

abline(lm(Exam_Score ~ Attendance,
          data = Performa_pembelajaran), col="red")

plot(Performa_pembelajaran$Sleep_Hours,
     Performa_pembelajaran$Exam_Score,
     main="Scatterplot Jam Tidur vs Nilai Ujian",
     xlab="Sleep Hours",
     ylab="Exam Score",
     pch=19,
     col="purple")

abline(lm(Exam_Score ~ Sleep_Hours,
          data = Performa_pembelajaran), col="red")