Ekonometrika

Exercise 1


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Nama Alicia Arifin
NIM 20214920001
Prodi Statistika, 2021

Exercise

GDP & Unemployment rate

Let’s consider a scenario where we want to analyze the relationship between a country’s GDP (Gross Domestic Product) and its unemployment rate. The hypothesis is that higher GDP leads to lower unemployment rates due to increased economic activity and job creation. First, we’ll generate a simulated dataset with two variables: GDP and unemployment rate. We’ll assume a linear relationship between the two variables with some random noise.

set.seed(123)

n=10000
gdp <- rnorm(n, mean =1000,sd=200)
unemployment <- 10-0.05*gdp+rnorm(n,mean=0,sd=2)

data<- data.frame(
  GDP=gdp,
  Unemployment=unemployment
)

head(data)

Your jobs:
1. Explore the data visually to understand the relationship between GDP and unemployment rate 2. Perform simple linear regression to quantify the relationship between GDP and unemployment rate 3. Interpret the relationship between GDP and unemployment rate.

1

Explore the data visually to understand the relationship between GDP and unemployment rate

# Make Correlation Matrix
library(corrplot)
corrplot(cor(data), method="number")

Correlation between Unemployment and GDP is -0.98.

library(ggplot2)
library(tidyverse)

ggplot(data, aes(x=GDP, y=Unemployment ))+
  geom_point(color="sky blue")+
  ggtitle("GDP vs Unemployment")

The hypothesis is that higher GDP leads to lower unemployment rates due to increased economic activity and job creation.
From the scatterplot above, accept hypothesis. higher the GDP, then the unemployement rate will be lower. The relation between variable are negative. The plot shows that the data makes a linear shape. Because of linear, we can use a simple regression linear.

2

Perform simple linear regression to quantify the relationship between GDP and unemployment rate

ggplot(data, aes(x=GDP, y=Unemployment ))+
  geom_point(color="orange")+
  geom_smooth(method = "lm")+
  ggtitle("GDP vs Unemployment")

summary(lm(unemployment~gdp))
## 
## Call:
## lm(formula = unemployment ~ gdp)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9652 -1.3378 -0.0148  1.3617  7.5393 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.9214218  0.1022358   97.04   <2e-16 ***
## gdp         -0.0499396  0.0001003 -497.89   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.003 on 9998 degrees of freedom
## Multiple R-squared:  0.9612, Adjusted R-squared:  0.9612 
## F-statistic: 2.479e+05 on 1 and 9998 DF,  p-value: < 2.2e-16

the linear regression from that data set are\[ Unemployment = 9.92 - 0.05 * GDP \] GDP has a statistically significant negative impact on Unemployment.

3

Interpret the relationship between GDP and unemployment rate.
Relationship between GDP and Unemployment rate is negative relation. If we want to decrease our unemployment rate, we must increase our GDP. the starting rate of unemployment is 9,92. GDP has an impact by negative 0,05.

GDP Growth Rate and Investment Rate

The objective of this study case is to demonstrate how simple linear regression can be used to analyze economic data and make predictions based on the relationship between two variables. Lets generate data for GDP growth rate (gdp_growth) and investment rate (investment_rate) for a fictional country over a period of 10 years.

set.seed(123)

years<- 1:10
invesment_rate <- rnorm(10,mean=20,sd=5)
gdp_growth <- 3 +0.8*invesment_rate+ rnorm(10,mean=0,sd=1)

data<- data.frame(years, invesment_rate, gdp_growth)
data

Your Jobs:
1. Perform simple linear regression analysis to understand the relationship between GDP growth rate and investment rate 2. Make predictions about future GDP growth rates based on different levels of investment 3. Gained insights into how changes in investment may influence economic growth.

1

Perform simple linear regression analysis to understand the relationship between GDP growth rate and investment rate

ggplot(data, aes(x=invesment_rate, y=gdp_growth ))+
  geom_point(color="#D24545")+
  geom_smooth(method = "lm")+
  ggtitle("Invesment Rate vs GDP Growth")

summary(lm(invesment_rate~gdp_growth))
## 
## Call:
## lm(formula = invesment_rate ~ gdp_growth)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.58676 -0.37809  0.05946  0.70065  1.15079 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.0498     1.4118   0.035    0.973    
## gdp_growth    1.0418     0.0707  14.736 4.42e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9535 on 8 degrees of freedom
## Multiple R-squared:  0.9645, Adjusted R-squared:   0.96 
## F-statistic: 217.1 on 1 and 8 DF,  p-value: 4.423e-07

The relationship between invesment rate and gdp growth is positive relationship. The Regression formula is invesment_rate = 0.0498 + 1.04 *gdp_growth. Invesment rate has a statistically significant impact on GDP growth.

2 & 3

Make predictions about future GDP growth rates based on different levels of investment
Gained insights into how changes in investment may influence economic growth.
Relationship between GDP growth and invesment rate is positive relation. More invesment rate goes up, GDP will continue to grow. The starting invesment rate is 0,0498. GDP growth has a positive impact by 1,0418 Unit if invesment rate increases per 1 unit.