Introduction

With the development of economy and urbanization, the dramatic changes of urban population have accelerated. This phenomenon is more common in megalopolises. People may move to cities for job opportunities or stay away from cities for better quality of life. At the same time as the population is changing, the house will switch between occupied and vacant. Meanwhile, housing prices will also be affected. In this research, we take the metropolitan area that New York City as an example, and show the plot and form of the changes in population, number of housing, housing value and household income in New York City. In addition, the method of regression analysis is used to explore the correlation between these variables. This study will propose three hypotheses: 1) The amount of urban population change is negatively related to the number of vacant houses;2) The value of the house is positively correlated with the income of the household; 3) The amount of change in urban population is positively correlated with house value. In order to verify the hypothesis, this study will use American Community Survey (ACS) Data from 2013-2018.

Materials and methods

Data: 1)Demographic data set of New York city from 2013-2018 2)Housing data set of New York city from 2013-2018 3)Economic datas et of New York city from 2013-2018

All data sets comes from American Community Survey (ACS) Data Tables and are in csv format.

The processes are descried in following steps.

1.Download the data. 2.Extract attributes from the data sets and integrate them in a single data set. 3.Visualize data. 4.Correlation analysis. 5.Test hypothesis.

Load any required packages in a code chunk.

library(tidyverse)
library(leaflet)
library(kableExtra)
library(dplyr)
library(ggplot2)
library(corrplot)
library(cowplot)
knitr::opts_chunk$set(cache=TRUE)  # cache the results for quick compiling

Read and summary data

options(scipen = 200)
datapath="./Dataset/NYC.csv"
nyc=read.csv(datapath)
nyc_whole<-nyc%>%filter(Area=="New York City")
each_county<-nyc%>%filter(Area!="New York City")
nyc %>% 
  slice(1:10) %>% #show only 1:n rows
  kable(digits=2,align="c")%>% #make table and round to two digits
  kable_styling(bootstrap_options = 
                  c("striped", "hover", "condensed", "responsive")) #apply other formatting
Area Year Total_population Occupied_housing Vacant_housing Median_value Median_income
New York City 2018 8,398,748 3,184,496 334,957 645,100 63,799
Bronx 2018 1,432,132 507,370 25,139 436,100 38,467
Brooklyn 2018 2,582,830 969,317 84,350 759,400 61,220
Manhattan 2018 1,628,701 752,258 134,024 1,013,400 85,066
Queens 2018 2,278,906 788,110 77,699 577,400 69,320
Staten Island 2018 476,179 167,441 13,745 556,000 82,166
New York City 2017 8,622,698 3,159,674 337,670 609,500 97,836
Bronx 2017 1,471,160 503,985 24,866 400,300 55,423
Brooklyn 2017 2,648,771 956,223 88,064 701,800 87,312
Manhattan 2017 1,664,727 764,218 122,166 976,100 151,745

Visualization and analysis of the data

First hypothesis

The change of the population and the number of vacant housing of NYC

p1<-nyc_whole%>%
  ggplot(aes(x=Year,y=Total_population,group=Area))+geom_line(size=1,color=2)+geom_point(size=3,color=4)+ylab('Population')+labs(title = 'The change of population in NYC')+
  theme(plot.title = element_text(hjust = 0.5))
p2<-nyc_whole%>%
  ggplot(aes(x=Year,y=Vacant_housing,group=Area))+geom_line(size=1,color=3)+geom_point(size=3,color=5)+ylab('The number of vacant housing')+labs(title = 'The change of vacant housing in NYC')+
  theme(plot.title = element_text(hjust = 0.5))
plot_grid(p1, p2)

The change of population and the number of vacant housing of each county

p3<-each_county%>%
  ggplot(aes(x=Year,y=Total_population,group=Area))+geom_line(size=1,color=2)+geom_point(size=3,color=4)+ylab('Population')+labs(title = 'The change of \n population in each county')+facet_wrap(~Area,scales="free_y",nrow=5,as.table = TRUE)+
  theme(plot.title = element_text(hjust = 0.5))
p4<-each_county%>%ggplot(aes(x=Year,y=Vacant_housing,group=Area))+geom_line(size=1,color=3)+geom_point(size=3,color=5)+ylab('The number of vacant housing')+labs(title = 'The change of \n vacant housing in each county')+facet_wrap(~Area,scales="free_y",nrow=5,as.table = TRUE)+
  theme(plot.title = element_text(hjust = 0.5))
plot_grid(p3, p4)

Second hypothesis

The change of median housing value and median household income of NYC

p5<-nyc_whole%>%
  ggplot(aes(x=Year,y=Median_value,group=Area))+geom_line(size=1,color=2)+geom_point(size=3,color=4)+ylab('Median value(dollors)')+labs(title = 'The change of \n median value of housing in NYC')+
  theme(plot.title = element_text(hjust = 0.5))
p6<-nyc_whole%>%
  ggplot(aes(x=Year,y=Median_income,group=Area))+geom_line(size=1,color=3)+geom_point(size=3,color=5)+ylab('Median household income(dollors)')+labs(title = 'The change of \n  median household income in NYC')+
  theme(plot.title = element_text(hjust = 0.5))
plot_grid(p5, p6)

The change of median housing value and median household income of each county

p7<-each_county%>%
  ggplot(aes(x=Year,y=Median_value,group=Area))+geom_line(size=1,color=2)+geom_point(size=3,color=4)+ylab('Population')+labs(title = 'The change of  median \n housing value in each county')+facet_wrap(~Area,scales="free_y",nrow=5,as.table = TRUE)+
  theme(plot.title = element_text(hjust = 0.5))
p8<-each_county%>%ggplot(aes(x=Year,y=Median_income,group=Area))+geom_line(size=1,color=3)+geom_point(size=3,color=5)+ylab('The number of vacant housing')+labs(title = 'The change of  median \n household income in each county')+facet_wrap(~Area,scales="free_y",nrow=5,as.table = TRUE)+
  theme(plot.title = element_text(hjust = 0.5))
plot_grid(p7, p8)

The third hypothesis

The change of population and median housing value of NYC

p9<-nyc_whole%>%
  ggplot(aes(x=Year,y=Total_population,group=Area))+geom_line(size=1,color=2)+geom_point(size=3,color=4)+ylab('Median value(dollors)')+labs(title = 'The change of \n population in NYC')+
  theme(plot.title = element_text(hjust = 0.5))
p10<-nyc_whole%>%
  ggplot(aes(x=Year,y=Median_value,group=Area))+geom_line(size=1,color=3)+geom_point(size=3,color=5)+ylab('Median value(dollors)')+labs(title = 'The change of \n median value of housing in NYC')+
  theme(plot.title = element_text(hjust = 0.5))
plot_grid(p9, p10)

The change of population and median housing value of each county

p11<-each_county%>%
  ggplot(aes(x=Year,y=Total_population,group=Area))+geom_line(size=1,color=2)+geom_point(size=3,color=4)+ylab('Population')+labs(title = 'The change of \n population in each county')+facet_wrap(~Area,scales="free_y",nrow=5,as.table = TRUE)+
  theme(plot.title = element_text(hjust = 0.5))
p12<-each_county%>%ggplot(aes(x=Year,y=Median_value,group=Area))+geom_line(size=1,color=3)+geom_point(size=3,color=5)+ylab('Median value(dollors)')+labs(title = 'The change of median value \n of housing in each county')+facet_wrap(~Area,scales="free_y",nrow=5,as.table = TRUE)+
  theme(plot.title = element_text(hjust = 0.5))
plot_grid(p11, p12)

Results

We use Pearson correlation cofficient to quantify the correlation between the two variables. When Pearson correlation cofficient approaches 1, it means that the two variables have a stronger positive correlation. When Pearson correlation cofficient approaches -1, it means that the two variables have a stronger negative correlation. When Pearson correlation cofficient approaches 0, that indicates the correlation between the two variables is weak.

population_vacant<-data.frame('Area'=c("New York City","Bronx","Brooklyn","Manhattan","Queens","Staten Island"),'Pearson correlation coefficient'=c(nyc_pop_vacant,bx_pop_vacant,bn_pop_vacant,mh_pop_vacant,q_pop_vacant,si_pop_vacant))
population_vacant%>%kable(digits=2,align="c",caption = "The pearson correlation cofficient between total of population and the number of vacant housing.",font_size = 17)%>% 
  kable_styling(bootstrap_options = 
                  c("striped", "hover", "condensed", "responsive"))
The pearson correlation cofficient between total of population and the number of vacant housing.
Area Pearson.correlation.coefficient
New York City 0.31
Bronx -0.70
Brooklyn 0.56
Manhattan -0.18
Queens 0.51
Staten Island 0.86 
value_income<-data.frame('Area'=c("New York City","Bronx","Brooklyn","Manhattan","Queens","Staten Island"),'Pearson correlation coefficient'=c(nyc_value_income,bx_value_income,bn_value_income,mh_value_income,q_value_income,si_value_income))
value_income%>%kable(digits=2,align="c",caption = "The pearson correlation cofficient between the median housing value and the median household income.",font_size = 17)%>% 
  kable_styling(bootstrap_options = 
                  c("striped", "hover", "condensed", "responsive"))
The pearson correlation cofficient between the median housing value and the median household income.
Area Pearson.correlation.coefficient
New York City 0.62
Bronx 0.44
Brooklyn 0.63
Manhattan 0.40
Queens 0.76
Staten Island 0.64 
pop_value<-data.frame('Area'=c("New York City","Bronx","Brooklyn","Manhattan","Queens","Staten Island"),'Pearson correlation coefficient'=c(nyc_pop_value,bx_pop_value,bn_pop_value,mh_pop_value,q_pop_value,si_pop_value))
pop_value%>%kable(digits=2,align="c",caption = "The pearson correlation cofficient between total of population and the median housing value.",font_size = 17)%>% 
  kable_styling(bootstrap_options = 
                  c("striped", "hover", "condensed", "responsive"))
The pearson correlation cofficient between total of population and the median housing value.
Area Pearson.correlation.coefficient
New York City 0.15
Bronx 0.03
Brooklyn -0.02
Manhattan 0.29
Queens -0.03
Staten Island 0.81

Conclusions

As the result of polts and tables, we can test the hypotheses.In the first hypothesis, we assume the amount of urban population change is negatively related to the number of vacant houses.From the study results,only the bronx county can fulfill this assumption. In the second hypothesis, we assume the value of the house is positively correlated with the income of the household.This assumption is basically true. In the third hypothesis, we can only find the amount of changing in urban population is positively correlated with house value in Manhattan and Staten Island.