get ps02

.gitignore

@@ -3,3 +3,4 @@ tutorials/.DS_Store
 problemSets/example/.Rhistory
 problemSets/.DS_Store
 .DS_Store
+.Rproj.user

problemSets/PS01/my_answers/PS01_DP.R

@@ -0,0 +1,200 @@
+#####################
+# load libraries
+# set wd
+# clear global .envir
+#####################
+
+# remove objects
+rm(list=ls())
+# detach all libraries
+detachAllPackages <- function() {
+  basic.packages <- c("package:stats", "package:graphics", "package:grDevices", "package:utils", "package:datasets", "package:methods", "package:base")
+  package.list <- search()[ifelse(unlist(gregexpr("package:", search()))==1, TRUE, FALSE)]
+  package.list <- setdiff(package.list, basic.packages)
+  if (length(package.list)>0)  for (package in package.list) detach(package,  character.only=TRUE)
+}
+detachAllPackages()
+
+# load libraries
+pkgTest <- function(pkg){
+  new.pkg <- pkg[!(pkg %in% installed.packages()[,  "Package"])]
+  if (length(new.pkg)) 
+    install.packages(new.pkg,  dependencies = TRUE)
+  sapply(pkg,  require,  character.only = TRUE)
+}
+
+# here is where you load any necessary packages
+# ex: stringr
+# lapply(c("stringr"),  pkgTest)
+
+lapply(c(),  pkgTest, "ggplot2")
+
+#####################
+# Problem 1
+#####################
+
+y <- c(105, 69, 86, 100, 82, 111, 104, 110, 87, 108, 87, 90, 94, 113, 112, 98, 80, 97, 95, 111, 114, 89, 95, 126, 98)
+
+# calculate the mean 
+mean_y = mean(y)
+mean_y
+
+# calculate the standard deviation 
+demeanedSum <- y - mean_y
+squaredError <- demeanedSum ^ 2 
+variance <- sum(squaredError)/(length(y)-1)
+stdev = sqrt(variance)
+stdev
+
+# calculate the standard error 
+sterror = stdev/sqrt(length(y))
+sterror
+
+# find the t-score for the desired confidence level 
+t = qt(p = (1 - 0.9)/2 , df = 24, lower.tail = FALSE)
+t 
+
+# construct the confidence interval 
+lowerlimit = mean_y - t * sterror
+upperlimit = mean_y + t * sterror
+lowerlimit
+upperlimit
+
+# hypothesis testing 
+# step 1 - assumptions: data is quantitative, sampling method is random, sample size is smaller than 30 -> t-score instead of z-score 
+
+# step 2- null hypothesis:  mean is lower or equal to 100 
+# alternative hypothesis: mean is higher than 100 
+
+# step 3 - calculate a test statistic
+ts = (mean_y - 100)/sterror
+ts 
+
+# step 4 - calculate the p-value 
+p = pt(ts, df = 24, lower.tail = FALSE)
+p
+
+# step 5 - conclusion 
+# p-value is higher than alpha -> cannot reject the null hypothesis that the mean is lower or equal to 100 
+
+
+#####################
+# Problem 2
+#####################
+lapply(c("ggplot2"), pkgTest)
+install.packages("ggpubr")
+library(ggpubr)
+
+expenditure <- read.table("https://raw.githubusercontent.com/ASDS-TCD/StatsI_2025/main/datasets/expenditure.txt", header=T)
+head(expenditure)
+
+# plot the relationships between all the variables 
+# add the correlation coefficient and hide the p-value
+# save the plots as a png to add to the latex file 
+
+png(file = "scatter_x1_y.pdf")
+ggplot(expenditure, aes(x = X1, y = Y)) +
+  geom_point() +
+  labs(title = "Relationship between personal income 
+  				and housing assistance expenditure",
+       x = "personal income (USD per capita)",
+       y = "expenditure on housing assistance (USD per capita)") +
+  stat_cor(aes(label = ..r.label..)) +
+  theme_minimal()
+dev.off()
+
+png(file = "scatter_x2_y.png")
+ggplot(expenditure, aes(x = X2, y = Y)) +
+  geom_point() +
+  labs(title = "Relationship between financial insecurity 
+  				and housing assistance expenditure",
+       x = "number of financially insecure residents (per 100,000)",
+       y = "expenditure on housing assistance (USD per capita)") +
+  stat_cor(aes(label = ..r.label..)) +
+  theme_minimal()
+dev.off()
+
+png(file = "scatter_x3_y.png")
+ggplot(expenditure, aes(x = X3, y = Y)) +
+  geom_point() +
+  labs(title = "Relationship between urban residency and 
+  				expenditure on housing assistance (in state)",
+       x = "number of urban residents (per 1000)",
+       y = "expenditure on housing assistance (USD per capita)") +
+  stat_cor(aes(label = ..r.label..)) +
+  theme_minimal()
+dev.off()
+
+png(file = "scatter_x1_x2.png")
+ggplot(expenditure, aes(x = X1, y = X2)) +
+  geom_point() +
+  labs(title = "Relationship between personal income 
+  				and financial insecurity",
+       x = "personal income (USD per capita)",
+       y = "number of financially insecure residents (per 100,000)")+
+  stat_cor(aes(label = ..r.label..)) +
+  theme_minimal()
+dev.off()
+
+png(file = "scatter_x1_x3.png")
+ggplot(expenditure, aes(x = X1, y = X3)) +
+  geom_point() +
+  labs(title = "Relationship between personal income 
+  				and urban residency",
+       x = "personal income (USD per capita)",
+       y = "number of urban residents (per 1000)") +
+  stat_cor(aes(label = ..r.label..)) +
+  theme_minimal()
+dev.off()
+
+png(file = "scatter_x2_x3.png")
+ggplot(expenditure, aes(x = X2, y = X3)) +
+  geom_point() +
+  labs(title = "Relationship between financial insecurity 
+  				and urban residency",
+       x = "number of financially insecure residents (per 100,000)",
+       y = "number of urban residents (per 1000)") +
+  stat_cor(aes(label = ..r.label..)) +
+  theme_minimal()
+dev.off()
+
+
+# turn the Region into a factor to make the plot more readable
+# now it shows the name of the region instead of 1,2,3,4
+expenditure$Region <- factor(expenditure$Region,
+  levels = c(1, 2, 3, 4),
+  labels = c("Northeast", "North Central", "South", "West"))
+
+# make a boxplot to compare the per capita housing expenditure in different regions 
+png(file = "boxplot_reg_y.png")
+ggplot(expenditure, aes(x=Region, y=Y, group=Region)) +
+   geom_boxplot() +
+   theme(
+      legend.position="none",
+      plot.title = element_text(size=11)) +
+      labs(title = "Boxplot for housing assistance expenditure for each region",
+           x = "Region",
+           y = "expenditure on housing assistance (USD per capita)") + 
+	theme_minimal()
+dev.off()
+
+# plot the relationship between x1, y and region
+# each region is represented by a different shape and colour
+png(file = "scatter_x1_y_reg.png")
+ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) +
+  geom_point(size = 3) +  # increase size to distinguish between the shapes 
+  scale_color_manual(values = c("black", "red", "green", "purple")) +
+  scale_shape_manual(values = c(21, 17, 18, 19)) +  # each value corresponds to a shape 
+  labs(title = "Relationship between personal income and 
+  				\n house assistance expenditure per region",
+       x = "personal income (USD per capita)",
+       y = "expenditure on housing assistance (USD per capita)",
+       shape = "Region", 
+       color = "Region") +
+  theme_minimal() +
+  theme(plot.title = element_text(hjust = 0.5)) # center title
+dev.off()
+
+
+
+

problemSets/PS01/my_answers/PS01_DP.aux

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