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# Sample Assignment Solution: Analyzing Default Probability and GDP Growth

In this sample assignment solution, we delve into two distinct data analysis tasks. First, we explore the prediction of customer default in credit card debt, employing a probit model to estimate the relationship between balance and default probability. The results provide insights into credit risk assessment. Next, we turn our attention to GDP growth analysis for Korea, visualizing historical trends and autocorrelations in GDP growth rates. We then make a prediction for GDP growth in the second quarter of 2023, showcasing the practical application of time series modeling. This sample provides a concise yet informative overview of these data analysis processes.

## 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.