## Problem Description:

In the data analysis assignment, we explore the prediction of default in a customer's credit card debt based on their balance using a probit model. We are provided with data in "Default.xlsx," which includes information on 10,000 observations with four variables: default (indicating whether the customer defaulted on their debt), student (indicating whether the customer is a student), balance (the average balance remaining after monthly payments), and income (customer's income).

## Question 1: Default Prediction

We estimate the probit model:

Pr(Default=1∣balance)=ϕ(β0+β1∗balance)

Given equation: Pr(Default=1∣balance)=ϕ(5.352−2.711∗balance)

The estimate for β1 is -2.711.

## Question 2: Scatter Plot of Predicted Probabilities

We visualize the relationship between predicted probabilities and balance with a scatter plot, placing balance on the horizontal axis.

**Fig 1: Scatter plot of predicted probabilities by balance**

**Question 3: GDP Growth Analysis
**

For this part of the assignment, we use data from "gdpgr_korea.xlsx," providing quarterly GDP growth data for Korea, where "GDPGR" is the annualized growth rate of real GDP (%).

**Question 3: Time Series Plot of GDP Growth
**

We create a time series plot of GDPGR to explore trends and fluctuations in Korea's GDP growth.

**Fig 2: Time Plot of GDPGR**

**Question 4: Autocorrelation Analysis**

We calculate the first autocorrelation of GDPGR to understand the dependence between GDP growth rates in consecutive quarters (result: 0.2808).

**Question 5: GDP Growth Prediction
**

Using an AR(2) model for GDPGR, we predict GDP growth in the second quarter of 2023, providing point forecasts and confidence intervals:

- Point Forecast for 2023 Q2: 1.012657
- 80% Confidence Interval: [-1.030577, 3.05589]
- 95% Confidence Interval: [-2.112199, 4.137512]

The estimated GDP growth for Q2 2023 is 1.01.