1. Loading Package

!pip install statsmodels==0.14.0

import pandas as pd import numpy as np from sklearn.model_selection import train_test_split from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression from sklearn.metrics import mean_squared_error from sklearn.preprocessing import StandardScaler import matplotlib.pyplot as plt from sklearn.metrics import mean_squared_error import statsmodels.api as sm from scipy.stats import ttest_1samp from scipy.stats import ttest_1samp from statsmodels.tsa.arima.model import ARIMA

# Read the CSV file df = pd.read_csv('Total.csv')

2.Cleaning Data

# Load the data data = pd.read_csv('Total.csv') # Drop any rows with missing values data = data.dropna() # Adjust the columns which are in percentage form percent_cols = ['GDP growth rate', 'Interest rate', 'Inflation rate', 'Unemployment rate'] for col in percent_cols: data[col] = data[col] * 0.01 # Standardize the 'Loans to private sector' for each country scaler = StandardScaler() data['Loans to private sector'] = data.groupby('country')['Loans to private sector'].transform(lambda x: scaler.fit_transform(x.values.reshape(-1,1)).flatten()) # Save the cleaned and standardized data data.to_csv('Data(Clean).csv', index=False)

3. Building Model

df = pd.read_csv('Data(Clean).csv') df_before = df[df['before or after'] == 'Before'] X_cols = ['GDP growth rate', 'Interest rate', 'Inflation rate', 'Unemployment rate', 'Residential property prices', 'Loans to private sector'] X = df_before[X_cols] y = df_before['Return rate'] # Split the data into training and validation set X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.3, random_state=42)

4. Get the best degree for regression

max_degree = 10 # I set up as 10 best_degree = 0 best_mse = np.inf for degree in range(1, max_degree+1): poly = PolynomialFeatures(degree=degree) X_train_poly = poly.fit_transform(X_train) X_val_poly = poly.transform(X_val) model = LinearRegression().fit(X_train_poly, y_train) predictions = model.predict(X_val_poly) mse = mean_squared_error(y_val, predictions) if mse < best_mse: best_mse = mse best_degree = degree print(f"Best polynomial degree is: {best_degree}")

5. Apporach the Model (evluate the model performance)

poly = PolynomialFeatures(degree=best_degree) X_poly = poly.fit_transform(X) model = LinearRegression().fit(X_poly, y) df_after = df[df['before or after'] == 'After'] X_after = df_after[X_cols] X_after_poly = poly.transform(X_after) predictions_after = model.predict(X_after_poly) actual_after = df_after['Return rate'] mse = mean_squared_error(actual_after, predictions_after) print(f"Mean Squared Error for 'after COVID' predictions: {mse}")

6. Draw the Difference between prediction and real

# Set up the figure and axis plt.figure(figsize=(10,6)) # Plot actual values plt.scatter(range(len(actual_after)), actual_after, color='blue', label='Actual', alpha=0.6) # Plot predicted values plt.scatter(range(len(predictions_after)), predictions_after, color='red', label='Predicted', alpha=0.6) # Labels and title plt.xlabel('Data Points') plt.ylabel('Return Rate') plt.title('Comparison between Actual and Predicted Return Rate (after COVID)') plt.legend() plt.show()

7. Anova & P-values & R-Squared

X_poly_with_const = sm.add_constant(X_poly) # adding a constant for the intercept model_sm = sm.OLS(y, X_poly_with_const).fit() print(model_sm.summary())

The regression results depict the relationship of multiple predictors to the return rate. With an value of 0.115, the model explains approximately 11.5% of the variance in the return rate. This suggests that while the predictors do have some explanatory power, a significant portion of the return rate's variability remains unexplained by the model. Among the predictors, variables labeled as x1 and x3 stand out as statistically significant at conventional levels (with p-values less than 0.05), implying a robust relationship with the return rate. Notably, the coefficients suggest that x1 has a positive correlation and x3 a negative correlation with the return rate. Conversely, other predictors such as x2, x4, x5, and x6 have high p-values, which denotes that their individual effects are not statistically distinguishable from zero within the model. The non-significant constant and high p-values for several predictors underscore the necessity for model refinement, potentially incorporating additional relevant predictors or considering other modeling techniques to enhance explanatory power.

8. Test if the differences between actual and predicted are significant

i). Draw The Difference

differences = actual_after - predictions_after plt.figure(figsize=(12,6)) # Plot the differences plt.bar(range(len(differences)), differences, color='purple', alpha=0.7) # Labels and title plt.xlabel('Data Points') plt.ylabel('Difference (Actual - Predicted)') plt.title('Differences between Actual and Predicted Return Rate (after COVID)') plt.axhline(0, color='black', linestyle='--') # zero line for reference plt.show()

ii). See the significant

t_stat, p_val = ttest_1samp(differences, 0) print(f"t-statistic: {t_stat}") print(f"p-value: {p_val}")

Given the t-statistic and p-value (more than 0.05 significant level), there's no statistically significant evidence to suggest that the parameters affecting the return rate are different before and after COVID-19, supporting your alternative hypothesis. However, always remember that "failing to reject" the null hypothesis doesn't prove the alternative hypothesis; it simply means that based on your data, the two periods (before and after COVID) are not statistically different in the context of return rates

9. View the equation

# Add a constant to the predictor matrix X = sm.add_constant(X) # Fit the OLS model model = sm.OLS(y, X).fit() # Extracting coefficients coefficients = model.params # Getting the equation equation = "Return rate = " for col, coef in coefficients.items(): if col == 'const': equation += f"{coef:.4f} + " else: equation += f"{coef:.4f}({col}) + " # Removing the last "+" equation = equation[:-3] print(equation)

Here is the equation then:

Return rate = -0.0002 + 1.2444(GDP growth rate) + -0.2153(Interest rate) + -2.7065(Inflation rate) + 0.9683(Unemployment rate) + -0.0000(Residential property prices) + -0.0032(Loans to private sector)

10. Effect Size of Parameters

# Standardize the predictors scaler = StandardScaler() X_standardized = pd.DataFrame(scaler.fit_transform(X), columns=X.columns) # Reset indices for both X_standardized and y to ensure alignment X_standardized.reset_index(drop=True, inplace=True) y.reset_index(drop=True, inplace=True) # Add a constant to the standardized predictor matrix X_standardized = sm.add_constant(X_standardized) # Fit the OLS model with standardized predictors model_standardized = sm.OLS(y, X_standardized).fit() # Extracting standardized coefficients beta_coefficients = model_standardized.params # Displaying standardized coefficients (beta values) print(beta_coefficients)

The effect sizes derived from the model shed light on the magnitudes of the relationships between predictors and the return rate. The GDP growth rate, with an effect size of 0.0637, indicates a relatively moderate positive relationship with the return rate. Conversely, the Inflation rate demonstrates a negative effect, suggesting that as inflation rises, the return rate tends to decrease. Unemployment rate and Residential property prices too exert negative pressures on the return rate, but their magnitudes are comparatively smaller. The interaction term between GDP and Interest rate showcases a negative effect size of -0.0236, implying that the combined influence of GDP growth and Interest rate has a dampening effect on the return rate. Interestingly, while the Interest rate and Loans to private sector both have effect sizes close to zero, suggesting minimal individual impact, their combined interaction reveals a more profound influence. This underscores the complexity of the relationships and the significance of understanding not just individual factors but also their interactions when predicting return rate

11. Time Series (AMRA) forcast future trend

# Create a function to predict using ARIMA def predict_arima(series, steps): model = ARIMA(series, order=(5,1,0)) model_fit = model.fit() forecast = model_fit.forecast(steps=steps) return forecast future_quarters = ['1', '2','3','4','5','6','7','8','9','10','11','12','13','14','15','16' ] # add all 16 future quarters here predictions = {} for country in df['country'].unique(): country_data = df[df['country'] == country] for col in ['GDP growth rate', 'Interest rate', 'Inflation rate', 'Unemployment rate', 'Residential property prices', 'Loans to private sector']: if country not in predictions: predictions[country] = {} predictions[country][col] = predict_arima(country_data[col], 16) # Use these predictions as input to the linear regression model linear_model = LinearRegression() # Assuming X_train and y_train have been defined earlier linear_model.fit(X_train, y_train) # Predict future return rates future_return_rates = {} for country in predictions: X_future = np.array(list(predictions[country].values())).T future_return_rates[country] = linear_model.predict(X_future) # Plot the results for country, rates in future_return_rates.items(): plt.plot(future_quarters, rates, label=country) plt.legend() plt.title('Predicted Return Rates') plt.show()