Team:
Amanda Gladys Bachtiar 1007972
Daniel Mangaraja Simanullang 1008043
Ng Zhao Hui 1007803
Tan Yi Le, Lydia 1008177
Thng Aik Kiat 1007781

Problem Statement:

In the 21st Century, how have employment rates in the healthcare industry and the elderly population been affected by the prevalence of AI?

Assumptions:
1) Venture Capital Investment in AI in recent years is correlated to the amount of research grant provided in the healthcare industry
2) Change in Population of Elderly is affected by research in the healthcare industry
3) Change in research grants lead to a change in manpower

Import CSV File into RStudio
Import necessary libraries for data visualization

library(readxl)
library(ggplot2)
library(rgl)
library(plotly)
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
data <- read_excel("C:/Users/USRR/OneDrive/Desktop/Term 2/Modelling Space and Systems/1D Materials/Math Modelling - Health care.xlsx")
summary(data)
##       Year      Principal Investigator Total Manpower /1000 65 and above /1000
##  Min.   :2014   Min.   :190.0          Min.   :12.30        Min.   :21.20     
##  1st Qu.:2016   1st Qu.:295.0          1st Qu.:22.00        1st Qu.:23.80     
##  Median :2018   Median :392.0          Median :28.60        Median :26.70     
##  Mean   :2018   Mean   :425.3          Mean   :25.57        Mean   :27.31     
##  3rd Qu.:2020   3rd Qu.:485.0          3rd Qu.:29.90        3rd Qu.:30.80     
##  Max.   :2022   Max.   :755.0          Max.   :33.30        Max.   :34.50     
##  NR Grant /1000  AHP Grant /1000   VCI in Ai      Total Grant /1000
##  Min.   :109.0   Min.   : 634    Min.   :  63.0   Min.   : 743     
##  1st Qu.:134.0   1st Qu.:1747    1st Qu.: 134.0   1st Qu.:1943     
##  Median :232.0   Median :1787    Median : 694.0   Median :2549     
##  Mean   :345.9   Mean   :2623    Mean   : 775.9   Mean   :2969     
##  3rd Qu.:424.0   3rd Qu.:4067    3rd Qu.: 714.0   3rd Qu.:4183     
##  Max.   :891.0   Max.   :5232    Max.   :2492.0   Max.   :5502     
##  VCA-Healthcare '000,000 USD Epmoyment in Healthcare and social services '000
##  Min.   :  0.22              Min.   :105.7                                   
##  1st Qu.:  6.90              1st Qu.:115.9                                   
##  Median : 42.00              Median :126.0                                   
##  Mean   : 75.74              Mean   :129.9                                   
##  3rd Qu.:117.00              3rd Qu.:139.9                                   
##  Max.   :229.00              Max.   :160.3

Finding the relationship between using Linear Regression

1 -Number of Principal Investigator ~ Year
2 -Total Manpower~Year
3 -Elderly Population ~ Year
4 -Total Grant for Research ~ Year
5 -Venture Capital Investment in Artificial Intelligence in Singapore ~ Year

fit1 = lm(data$`Principal Investigator`~ data$Year, data = data)
fit2 = lm(data$`Epmoyment in Healthcare and social services '000`~ data$Year, data = data)
fit3 = lm(data$`65 and above /1000`~ data$Year, data = data)
fit4 = lm(data$`Total Grant /1000`~ data$Year, data = data)
fit5 = lm(data$`VCA-Healthcare '000,000 USD`~ data$Year + I(data$Year^2)+ I(data$Year^3))
fit6 = lm(data$`Principal Investigator`~data$`Epmoyment in Healthcare and social services '000`, data = data)
fit7 = lm(data$`Principal Investigator`~ data$`VCA-Healthcare '000,000 USD`+ data$`Epmoyment in Healthcare and social services '000`)

Plotting Number of Principal Investigator from 2014 to 2022

fitt = plot(data$`Principal Investigator`~ data$Year, data = data, xlab = "Year" , ylab = "Number of Principal Investigator ")+
  abline(fit1, col = "red")

## Conclusion: Number of Principle Investigators generally increase over the years

Plotting Number of Principal Investigator ’000 compared to Total Manpower ’000

plot(data$`Principal Investigator`~ data$`Epmoyment in Healthcare and social services '000`, data = data, xlab = "Total Manpower in Healthcare Sector '000" , ylab = "Number of Principal Investigator '000")+
  abline(fit6, col = "red")

## integer(0)

Conclusion:

Generally, number of principal investigator increases with respect to total manpower.

Plotting Total Manpower (Healthcare) from 2014 to 2022

plot(data$`Epmoyment in Healthcare and social services '000`~ data$Year, data = data, xlab = "Year", ylab= "Total Manpower (Healthcare) '000")+
  abline(fit2, col = "red")

## integer(0)

Conclusion:

Total Manpower (Healthcare) increases linearly over the years

Plotting Elderly Population (Aged 65 and above) from 2014 to 2022

plot(data$`65 and above /1000`~ data$Year, data = data, xlab = "Year", ylab= "Elderly Population (Above 65) '000")+
  abline(fit3, col = "red")

## integer(0)

Conclusion:

Elderly Population increases linearly across the year

Plotting Total Research Grant in SingHealth from 2014 to 2022

plot(data$`Total Grant /1000`~ data$Year, data = data, xlab = "Year", ylab= "Total Research Grant")+
  abline(fit4, col = "red")

## integer(0)

##Conclusion: There is no visible correlation between Research Grant over the years

Plotting Total Investment in AI (Healthcare) from 2014 to 2022

pred= predict(fit5, newdata = list(data$Year))
plot(data$`VCA-Healthcare '000,000 USD`~ data$Year, data = data, xlab = "Year", ylab= "Investment in AI (Healthcare) in Million USD")+
  lines(data$Year,pred, col = "red", type = )

## integer(0)

##Conclusion: There is an exponential growth in terms of investment in AI in Singapore over the years

Plotting Multiple linear Regressions

lm.fit = lm(data$`VCI in Ai`~ data$`Total Grant /1000` + data$`Epmoyment in Healthcare and social services '000`, data = data)
summary(lm.fit)
## 
## Call:
## lm(formula = data$`VCI in Ai` ~ data$`Total Grant /1000` + data$`Epmoyment in Healthcare and social services '000`, 
##     data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -439.00 -303.16  -59.87  256.56  722.55 
## 
## Coefficients:
##                                                           Estimate Std. Error
## (Intercept)                                             -4558.0870  1128.7118
## data$`Total Grant /1000`                                   -0.0537     0.1015
## data$`Epmoyment in Healthcare and social services '000`    42.2787     9.5465
##                                                         t value Pr(>|t|)   
## (Intercept)                                              -4.038  0.00682 **
## data$`Total Grant /1000`                                 -0.529  0.61571   
## data$`Epmoyment in Healthcare and social services '000`   4.429  0.00443 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 444.4 on 6 degrees of freedom
## Multiple R-squared:  0.7968, Adjusted R-squared:  0.729 
## F-statistic: 11.76 on 2 and 6 DF,  p-value: 0.008395

Conclusion:

There is a correlation for Venture Capital investment in Artificial Intelligence and the Total Manpower in SingHealth.

Plot 3D graph:

X axis - Total Manpower ’000
Y axis - Total Research Grant ’000
Z axis - Investment in AI (Healthcare) in Millions (USD)

p <- plot_ly(
  data, x = data$`Total Manpower /1000`, y =data$`Total Grant /1000`,z=data$`VCA-Healthcare '000,000 USD`, 
  color = data$Year, colors = c('lightblue', 'red')
  ) %>%
  add_markers() %>%
  layout(
    scene = list(xaxis = list(title = "Total Manpower '000"),
        yaxis = list(title = "Total Grant '000'"),
        zaxis = list(title = "VCI in AI in million (USD)"))
        )
p

Conclusion:

As the years go by, total number of manpower increases, amount of research grant increases and Investment in AI(Healthcare) increases.

Plot 3D graph:

X axis - Total Manpower ’000
Y axis - Total Research Grant ’000
Z axis - Population of Elderly (Above 65 years old)

p <- plot_ly(
  data, x = data$`Total Manpower /1000`, y =data$`Total Grant /1000`,z=data$`65 and above /1000`, 
  color = data$Year, colors = c('lightblue', 'red')
  ) %>%
  add_markers() %>%
  layout(
    scene = list(xaxis = list(title = "Total Manpower '000"),
        yaxis = list(title = "Total Grant '000'"),
        zaxis = list(title = "Population of Elderly '000"))
        )
p

Conclusion:

As the years go by, total number of manpower increases, amount of research grant increases and population of elderly increases.

Plot 3D graph:

X axis - Number of Principal Investigator
Y axis - Venture Capital Investment in Healthcare (in million USD)
Z axis - Employment in Healthcare and Social Services ’000

p <- plot_ly(
  data, x = data$`Principal Investigator`, y =data$`VCA-Healthcare '000,000 USD` ,z=data$`Epmoyment in Healthcare and social services '000` , color = data$Year, colors = c('lightblue', 'red')) %>%
  add_markers() %>%
  layout(
    scene = list(xaxis = list(title = "Number of PI"),
        yaxis = list(title = "Investment in AI (in million USD)"),
        zaxis = list(title = "Employment'000"))
        )
p

Conclusion:

Over the years, we can se that the number of principal investigator together with venture capital investment in AI in the healthcare industry and the employment in healthcare industry increases over time from 2014 to 2022.

Conclusion of Problem Statement:

In conclusion, it is still insufficient to conclude with the data on hand as the data may be correlated but independent of one another. Assumptions in these models are that the variables are dependent on one another such that the investment in artificial intelligence is proportional to the amount of research grant received by SingHealth and that it creates more jobs as a result of investment in the healthcare industry. However, more conclusive data is needed to come to a conclusion that investment in AI will lead to more jobs in the healthcare industry.