RPubs link information

• Rpubs link comes as below:

Introduction

• In this project, we aim to test if there is a linear relationship of GDP and total population of a country.
• The assumption is that GDP has linear relationship with total population of a country.

Problem Statement

• It is reasonale to assume a positive relationship between GDP and Population
• Using statitical methods to gain statistic evidence that this reloationship is linear
• scatter plot and linear regression model in R are the predominant methods in this project

Data

• Data from 264 countries are extracted from data.world (https://data.world) for this investigation.
• GDP (Gross Domestic Product) - sum value of all goods and services produced in the country
• GDP PPP (GDP at Purchasing power parity) - GDP valued at prices prevailing in United States
• Total population - population data in 2015

World <- read_excel("2015 World Bank data by nation and region.xls")

Data Cont.

• Data has been subset to only include complete records
• Total population is highly right skewed

colnames(World)[4] <- "GDP_PPP"
colnames(World)[5] <- "Total_population"
Worldnew <- World[!is.na(World$GDP_PPP),]
Worldnew$GDP_PPP %>% hist(main = "GDP-PPP")

Data Cont.

• Scatter Plot

plot(GDP_PPP ~ Total_population, data = Worldnew)

Data Transformation

• The Log transformation is applied here to make this highly right skewed distributions less skewed

Worldnew$GDP_PPP <- Worldnew$GDP_PPP %>% log()
Worldnew$Total_population <- Worldnew$Total_population %>% log()

Descriptive Statistics and Visualisation

• Total number of observations is 214 with population range from 9 - 23 and GDP from 19 - 33.
• Log scale is applied.
• The sccater plot indicates a possible linear relationship between two variables.

plot(GDP_PPP ~ Total_population, data = Worldnew,xlab = "Total Population(Log scaled)",ylab = "GDP_PPP(Log scaled)")
abline(lm(GDP_PPP ~ Total_population, data = Worldnew), col = "RED")

Decsriptive Statistics Cont.

• See summary statitics below;

Worldnew %>% summarise(Min = min(GDP_PPP,na.rm = TRUE),
                                           Q1 = quantile(GDP_PPP,probs = .25,na.rm = TRUE),
                                           Median = median(GDP_PPP, na.rm = TRUE),
                                           Q3 = quantile(GDP_PPP,probs = .75,na.rm = TRUE),
                                           Max = max(GDP_PPP,na.rm = TRUE),
                                           Mean = mean(GDP_PPP, na.rm = TRUE),
                                           SD = sd(GDP_PPP, na.rm = TRUE),
                                           n = n(),
                                           Missing = sum(is.na(GDP_PPP))) -> table1
knitr::kable(table1)

Hypothesis Testing

• The linear regression statistical hypotheses is as following:

\[H_0: data \ do \ not \ fit \ linear \ regression \ model \] \[H_A: data \ fit \ linear \ regression \ model \]

gdpmodel <- lm(GDP_PPP ~ Total_population, data = Worldnew)
gdpmodel %>%  summary()

## 
## Call:
## lm(formula = GDP_PPP ~ Total_population, data = Worldnew)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9777 -0.7941  0.1847  0.8259  2.4725 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      10.02404    0.49925   20.08   <2e-16 ***
## Total_population  0.95756    0.02939   32.58   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.14 on 212 degrees of freedom
## Multiple R-squared:  0.8335, Adjusted R-squared:  0.8327 
## F-statistic:  1061 on 1 and 212 DF,  p-value: < 2.2e-16

gdpmodel %>% confint()

##                      2.5 %    97.5 %
## (Intercept)      9.0399088 11.008177
## Total_population 0.8996238  1.015497

Hypthesis Testing Cont.

• Assumptions(See next slides for visualization)

1. Independence
   • Assumed as each observation comes from one country
2. Linearity
   • Scatter plot between GDP and population suggest linearity
   • Residual vs Fitted plot also shows the roughly flat relationship
3. Normality of residuals
   • No significant deviation from normal distribution from Q-Q plot
4. Homoscedasticity
   • From scope locale plot the red line appears to be roughly flat.
   • Residuals are randomly spread, with variance relatively consistent across fitted values.
5. Influential cases
   • According to Residuals vs Leverage plot, no influential cases present in data set

Hypthesis Testing Cont.

plot(gdpmodel)

Discussion

• The linear model was statistically significant, F(1,212) = 1061, p < .001. H0 is rejected.
• Population of the country explained 83.35 % of the GDP_PPP.
• The estimated average GDP when population = 0 was 10.02, 95% CI (9.04, 11.01), the intercept of the regression as statistically significant
• For every one unit increase in population, GDP increases on average by 0.96, 95% CI (0.90, 1.02)
• The slope of regression for population was statistically significant, b= 0.96, p < 0.001
• The estimated regression equation was: \[y = 10.02 + 0.9*x \]

Limitations

• potentially biased by relatively large number of missing value
• data only represents year 2015

Conclusion:

• There is statistically significant linear postive relationship between GDP PPP and total population.
• The findings agree to our initial assumption.
• For future investigations, the above equation can be tested by inputting data from larger time span

References

• Gary, H. (2016). 2015 World Bank data by nation and region. Retrieved from https://data.world/garyhoov/world-bank-data/workspace/file?filename=2015+World+Bank+data+by+nation+and+region.xls
• CIA. (2018). The World Factbook. Retrieved from https://www.cia.gov/library/publications/the-world-factbook/fields/208rank.html#:~:text=A%20nation’s%20GDP%20at%20purchasing,prevailing%20in%20the%20United%20States.