First commit

Project.R

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+# Task 1
+
+
+# b)
+X <- 0:12
+Y <- dgeom(X, p = 0.45)
+plot(X, Y, type = "h", main = "Geometric distribution (p=0.45)", ylab = "P(X=k)")
+points(X, Y, pch = 16)
+
+# Task 2
+
+# b)
+X <- 0:30
+Y <- dbinom(X, size = 30, prob = .6)
+plot(X, Y, type = "h", main = "Binominal distribution (p=0.6)", ylab = "P(X=k)")
+points(X, Y, pch = 16)
+
+# Task 3
+
+# 2)
+X <- 0:40
+Y <- dpois(X, lambda = 20)
+plot(X, Y, type = "h", main = "Poisson distribution (lambda=20)", ylab = "P(X=k)")
+points(X, Y, pch = 16)
+
+# Task 4
+library(readr)
+data_set1 <- read_csv("data_set1.csv")
+View(data_set1)
+
+# 1) The name of the column is "Val".
+# 2) There are 1029 rows.
+# 3) Max = 109.379
+max(data_set1)
+# 4) Min = 4.193534
+min(data_set1)
+# 5) Mean = 50.49665
+mean(data_set1$Val)
+# 6) Median = 50.52415
+median(data_set1$Val)
+# 7) Variance = 218.7175
+var(data_set1$Val)
+# 8) Standard deviation = 14.7891
+sd(data_set1$Val)
+
+# Task 5
+# 1)
+library(readr)
+data_set1 <- read_csv("data_set1.csv")
+X <- 0:100
+Y <- dnorm(X, mean = mean(data_set1$Val), sd = sd(data_set1$Val))
+plot(X, Y, type = "l", ylim = c(0, 0.03), main = "Data set vs normal distribution")
+# 2)
+d <- density(data_set1$Val, bw = 3)
+# 3)
+points(d, col = "red", type = "l")
+# 4)
+abline(v = mean(data_set1$Val), col = "green")
+
+# Task 6
+# 4 variables most correlated with hp: mpg, cyl, disp, carb
+cars <- mtcars
+round(cor(cars), digits = 2)
+
+# Task 7
+# 1)
+model <- lm(hp ~ cyl + disp + carb + mpg, data = mtcars)
+# 2)
+hp_hat <- predict(model)
+# 3)
+residuals <- mtcars$hp - hp_hat
+# 4)
+hpplot <- density(residuals)
+plot(hpplot, main = "Density of residuals")
+# 6)
+summary(model)$r.squared # 0.8594845 - Correct and accurate
+
+# Task 8
+library(readr)
+data_set2 <- read_csv("data_set2.csv")
+X <- min(data_set2):max(data_set2)
+Y <- dnorm(X, mean = mean(data_set2$Val), sd = sd(data_set2$Val))
+plot(X, Y, type = "l", main = "Normal distribution of stick lengths")
+d <- density(data_set2$Val, bw = 1)
+points(d, col = "red", type = "l")
+abline(v = mean(data_set2$Val), col = "green")
+# The length of the sticks is not acceptable as the mean is much higher than the null hypothesis of µ = 30 and most values are not around 30.