No.3
set.seed(42)
x1 <- rnorm(100)
x2 <- x1 + rnorm(100, 0, 0.01)
x3 <- rnorm(100)
y <- 3 + 2*x1 - 1*x3 + rnorm(100)
model <- lm(y ~ x1 + x2 + x3)
summary(model)
##
## Call:
## lm(formula = y ~ x1 + x2 + x3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7944 -0.5867 -0.1038 0.6188 2.3280
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.03150 0.08914 34.007 <2e-16 ***
## x1 1.17483 9.89434 0.119 0.906
## x2 0.88292 9.89031 0.089 0.929
## x3 -1.03161 0.08882 -11.614 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8867 on 96 degrees of freedom
## Multiple R-squared: 0.8927, Adjusted R-squared: 0.8893
## F-statistic: 266.2 on 3 and 96 DF, p-value: < 2.2e-16
No.4
set.seed(123)
data <- rnorm(100, mean=70, sd=5)
max_value <- max(data)
max_value
## [1] 80.93666
No.5
set.seed(123)
categories <- c("A", "B", "C")
probabilities <- c(0.2, 0.3, 0.5)
sample_data <- sample(categories, size=100, replace=TRUE, prob=probabilities)
count_b <- sum(sample_data == "B")
count_b
## [1] 29
No.6
set.seed(123)
x <- rnorm(100)
y <- 2*x + rnorm(100)
model <- lm(y ~ x)
summary(model)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9073 -0.6835 -0.0875 0.5806 3.2904
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.10280 0.09755 -1.054 0.295
## x 1.94753 0.10688 18.222 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9707 on 98 degrees of freedom
## Multiple R-squared: 0.7721, Adjusted R-squared: 0.7698
## F-statistic: 332 on 1 and 98 DF, p-value: < 2.2e-16
No.7
set.seed(123)
data <- rnorm(100, mean=50, sd=10)
std_deviation <- sd(data)
std_deviation
## [1] 9.128159
No.8
set.seed(123)
x <- c(5, 7, 8, 10, 12)
n_bootstrap <- 1000
bootstrap_means <- numeric(n_bootstrap)
for (i in 1:n_bootstrap) {
sample_x <- sample(x, size = length(x), replace = TRUE)
bootstrap_means[i] <- mean(sample_x)
}
mean_bootstrap <- mean(bootstrap_means)
mean_bootstrap
## [1] 8.3572
No.9
set.seed(123)
data <- rexp(100, rate = 1)
median_data <- median(data)
median_data
## [1] 0.847754
No.11
set.seed(123)
data <- runif(100, min = 20, max = 80)
data_range <- max(data) - min(data)
data_range
## [1] 59.6187
No.12
set.seed(123)
data <- rbinom(100, size = 10, prob = 0.3)
mean_data <- mean(data)
mean_data
## [1] 3.02
No.13
set.seed(123)
data <- rpois(100, lambda = 4)
table_data <- table(data)
modus <- as.numeric(names(table_data)[which.max(table_data)])
modus
## [1] 2
No.14
set.seed(123)
data <- rbinom(1000, size = 10, prob = 0.3)
mean_succes <- mean(data)
mean_succes
## [1] 2.989
No.15
set.seed(123)
data <- rnorm(100)
mean_data <- mean(data)
sd_data <- sd(data)
outliers <- sum(data < (mean_data - 2 * sd_data) | data > (mean_data + 2 * sd_data))
outliers
## [1] 5
No.16
set.seed(123)
x <- c(5, 8, 12, 13, 15, 18, 21)
n_bootstrap <- 10000
bootstrap_medians <- numeric(n_bootstrap)
for (i in 1:n_bootstrap) {
sample_x <- sample(x, size = length(x), replace = TRUE)
bootstrap_medians[i] <- median(sample_x)
}
ci <- quantile(bootstrap_medians, probs = c(0.025, 0.975))
ci
## 2.5% 97.5%
## 8 18
No.17
set.seed(123)
data <- rnorm(100, mean = 0, sd = 1)
filtered_data <- data[data > 1]
length(filtered_data)
## [1] 17
No.18
rnorm(100, 70, 15)
## [1] 59.34390 73.85326 66.29962 64.78686 55.72572 69.32458 58.22643
## [8] 44.98087 64.29660 83.78495 61.36980 79.11946 45.73176 69.16657
## [15] 77.79111 74.51730 71.58514 60.38941 57.25443 54.63807 71.76470
## [22] 55.78788 62.64164 66.15862 97.65793 60.22075 73.53080 71.16941
## [29] 55.57215 68.93038 91.66826 76.77256 70.61849 63.66255 39.20129
## [36] 86.97006 48.09040 81.09921 98.63655 48.34160 80.52677 66.06704
## [43] 46.41784 47.27999 45.97696 62.03640 48.07367 80.31875 101.50163
## [50] 50.69454 81.81608 81.53563 74.98304 54.87435 68.20821 65.79407
## [57] 78.44484 64.41342 84.65460 64.38129 85.79067 54.26234 51.09767
## [64] 118.61560 63.74714 74.47341 79.54855 62.74329 77.75293 75.53447
## [71] 66.76929 70.97940 69.48899 101.92678 58.87996 53.56006 70.56683
## [78] 74.65721 76.54785 63.12452 54.05011 88.94778 64.75524 57.01731
## [85] 66.45581 67.04236 86.64880 71.27106 81.31081 62.51062 73.21668
## [92] 65.12971 71.41875 56.56955 50.33798 99.95820 79.01063 51.23093
## [99] 60.83251 52.21780
No.19
set.seed(123)
data1 <- rnorm(50, mean = 100, sd = 15)
data2 <- rnorm(50, mean = 80, sd = 10)
combined_data <- c(data1, data2)
mean_combined <- mean(combined_data)
mean_combined
## [1] 90.99007
No.20
set.seed(123)
x <- 1:10
y <- 2 * x + rnorm(10, mean = 0, sd = 1)
model <- lm(y ~ x)
slope <- coef(model)[["x"]]
slope
## [1] 1.918029
No.21
# Distribusi Poisson
No.22
# Distribusi Normal
No.23
# Efektif untuk memodelkan jumlah kejadian dalam interval waktu tetap
No.24
# Poisson mengasumsikan kedatangan independen, yang tidak terpenuhi
No.25
# Efisien untuk memodelkan proporsi keberhasilan dari sejumlah percobaan