Soal UAS 2 Analisis Regresi

1 Persiapan awal

1.1 Library

library(readxl)
library(ggplot2)
library(dplyr)

1.2 Mengatur Working Directory

setwd("C:/Users/vferd/Documents/Sherly/Campus/Semester 3/Analisis Regresi/w11")
getwd()

## [1] "C:/Users/vferd/Documents/Sherly/Campus/Semester 3/Analisis Regresi/w11"

1.3 Membaca Data

MS <- read.csv("belajar komputer.csv", sep = ";")
MS

##    ï..id num.responses cost
## 1      1            16   77
## 2      2            14   70
## 3      3            22   85
## 4      4            10   50
## 5      5            14   62
## 6      6            17   70
## 7      7            10   55
## 8      8            13   63
## 9      9            19   88
## 10    10            12   57
## 11    11            18   81
## 12    12            11   51

2 Uji Heterokedastisitas

2.1 Scatter plot

ggplot(MS, aes(y = cost, x = num.responses)) +
  geom_point() +
  geom_smooth(method = lm, se = FALSE,
              color = "black", 
              size = 0.5, 
              linetype = "dashed") +
  labs(title = "Scatterplot of cost ~ num.reponses")

2.2 Mencocokkan model cost~num.responses

MS.lm <- lm(cost ~ num.responses, data = MS)
summary.lm(MS.lm)$coefficients

##                Estimate Std. Error  t value     Pr(>|t|)
## (Intercept)   19.472689  5.5161841 3.530101 5.445888e-03
## num.responses  3.268908  0.3650515 8.954649 4.330241e-06

paste("R2: ", round(summary.lm(MS.lm)$r.squared, 3))

## [1] "R2:  0.889"

2.3 Membuat plot dari model regresi

data.frame(y = rstandard(MS.lm),
           x = MS.lm$fitted.values) %>%
  ggplot(aes(x = x, y = y)) + 
  geom_point() +
  geom_hline(yintercept = 0, linetype = "dotted") +
  labs(title = "Standardized Residuals vs Fitted Values Plot")

3 Metode WLS

3.1 Mencari model regresi baru

MS.weights <- 1 / lm(abs(MS.lm$residuals) ~ MS.lm$fitted.values)$fitted.values^2
MS.lmw <- lm(cost ~ num.responses, 
              data = MS, 
              weights = MS.weights)
summary.lm(MS.lmw)$coefficients

##                Estimate Std. Error  t value     Pr(>|t|)
## (Intercept)   17.300637   4.827736 3.583592 4.981868e-03
## num.responses  3.421106   0.370310 9.238492 3.268919e-06

paste("R2: ", round(summary.lm(MS.lmw)$r.squared, 3))

## [1] "R2:  0.895"

3.2 scatterplot

data.frame(y = rstandard(MS.lmw),
           x = MS.lm$fitted.values) %>%
  ggplot(aes(x = x, y = y)) + 
  geom_point() +
  geom_hline(yintercept = 0, linetype = "dotted") +
  labs(title = "Standardized Residuals vs Fitted Values Plot")

4 Perbandingan plot OLS dan WLS

ggplot(data = MS, aes(y = cost, x = num.responses)) +
  geom_point() +
  geom_smooth(method = lm, se = FALSE,
              color = "black", 
              size = 0.5, 
              linetype = "dashed") +
  geom_smooth(method = lm, se = FALSE, 
              aes(weight = MS.weights),
              color = "red", 
              size = 0.5,
              linetype = "dashed") +
  labs(title = "Scatterplot of cost ~ num.reponses")

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'