From 4aaaaebb94ee63a4960b73c59f00b7f6be5e5583 Mon Sep 17 00:00:00 2001 From: Andrew Trieu <68151686+AndrewTrieu@users.noreply.github.com> Date: Fri, 25 Nov 2022 14:32:21 +0200 Subject: [PATCH] First commit --- Project.R | 87 ++ Statistical mathematics project work.pdf | Bin 0 -> 220002 bytes data_set1.csv | 1030 +++++++++++++++++++ data_set2.csv | 1201 ++++++++++++++++++++++ 4 files changed, 2318 insertions(+) create mode 100644 Project.R create mode 100644 Statistical mathematics project work.pdf create mode 100644 data_set1.csv create mode 100644 data_set2.csv diff --git a/Project.R b/Project.R new file mode 100644 index 0000000..aa2be7d --- /dev/null +++ b/Project.R @@ -0,0 +1,87 @@ +# 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 ยต = 30 and most values are not around 30. \ No newline at end of file diff --git a/Statistical mathematics project work.pdf 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