library(csvread)
library(car)
## Loading required package: carData
library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.6 v dplyr 1.0.7
## v tidyr 1.1.4 v stringr 1.4.0
## v readr 2.1.0 v forcats 0.5.1
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x dplyr::recode() masks car::recode()
## x purrr::some() masks car::some()
data <- read.csv("D:/STATISTIKA IPB/SEMESTER 4/ANALISIS REGRESI/Student_Marks.csv")
data <- data[,-1]
colnames(data) <- c("Time Study", "Marks")
names(data)
## [1] "Time Study" "Marks"
#Model Regresi
model.regresi <- lm(Marks~`Time Study`, data=data)
summary(model.regresi)
##
## Call:
## lm(formula = Marks ~ `Time Study`, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.866 -4.034 -0.384 2.979 10.628
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2239 0.9623 1.272 0.206
## `Time Study` 5.6888 0.2042 27.853 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.822 on 98 degrees of freedom
## Multiple R-squared: 0.8878, Adjusted R-squared: 0.8867
## F-statistic: 775.8 on 1 and 98 DF, p-value: < 2.2e-16
#Anova
anova(model.regresi)
## Analysis of Variance Table
##
## Response: Marks
## Df Sum Sq Mean Sq F value Pr(>F)
## `Time Study` 1 18039.9 18039.9 775.77 < 2.2e-16 ***
## Residuals 98 2278.9 23.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Selang Kepercayaan Parameter Regresi
#B0
confint(model.regresi, "(Intercept)", 0.95)
## 2.5 % 97.5 %
## (Intercept) -0.6857583 3.133475
#B1
confint(model.regresi, "`Time Study`", 0.95)
## 2.5 % 97.5 %
## `Time Study` 5.283434 6.094067
plot(data$`Time Study`, data$Marks)
abline(model.regresi, col="blue", lwd=2)
cor(data$`Time Study`, data$Marks)
## [1] 0.9422539
#Ukuran Keragaman
jkg <- sum((data$`Time Study` - model.regresi$fitted.values)^2)
jkr <- sum((model.regresi$fitted.values - mean(data$`Time Study`))^2)
jkt <- sum((data$`Time Study` - mean(data$`Time Study`))^2)
jkt2 <- jkr+jkg
#Uji hipotesis
alpha = 0.05
n = dim(data)[1]
#Uji t
#H0 : beta_1 = 0
summary(model.regresi)
##
## Call:
## lm(formula = Marks ~ `Time Study`, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.866 -4.034 -0.384 2.979 10.628
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2239 0.9623 1.272 0.206
## `Time Study` 5.6888 0.2042 27.853 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.822 on 98 degrees of freedom
## Multiple R-squared: 0.8878, Adjusted R-squared: 0.8867
## F-statistic: 775.8 on 1 and 98 DF, p-value: < 2.2e-16
t_crit <- abs(qt(alpha/2, n-2))
t_crit
## [1] 1.984467
colnames(data) <- c("x","y")
model.regresi <- lm(y ~ x, data=data)
#1. Ukuran Kebaikan Model (R-squared)
#melihat dari summary model
summary(model.regresi)
##
## Call:
## lm(formula = y ~ x, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.866 -4.034 -0.384 2.979 10.628
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2239 0.9623 1.272 0.206
## x 5.6888 0.2042 27.853 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.822 on 98 degrees of freedom
## Multiple R-squared: 0.8878, Adjusted R-squared: 0.8867
## F-statistic: 775.8 on 1 and 98 DF, p-value: < 2.2e-16
#2. Prediksi Nilai Y dan SK
#memasukkan x tertentu
newdata <- data.frame(x=6)
#SK bagi individu
predict(model.regresi, newdata, interval = "prediction")
## fit lwr upr
## 1 35.35636 25.7075 45.00522
#SK bagi rataan y
predict(model.regresi, newdata, interval = "confidence")
## fit lwr upr
## 1 35.35636 34.12219 36.59053