import pandas as pd import numpy as np import matplotlib.pyplot as plt import seaborn as sns import statsmodels.api as sm from scipy.stats import probplot from scipy import stats from statsmodels.stats.outliers_influence import variance_inflation_factor sns.set_style("whitegrid")

happiness = pd.read_csv('WHR20_DataForFigure2.1.csv') data = happiness.drop(['Standard error of ladder score','upperwhisker', 'lowerwhisker', 'Ladder score in Dystopia', 'Explained by: Log GDP per capita', 'Explained by: Social support', 'Explained by: Healthy life expectancy', 'Explained by: Freedom to make life choices', 'Explained by: Generosity', 'Explained by: Perceptions of corruption', 'Dystopia + residual'], axis='columns')

data.describe()

sns.distplot(data['Ladder_score']) plt.xlabel('Ladder score') plt.title('Distribution of ladder scores') plt.show() print("Figure 2: A histogram of the ladder scores")

formula_string = "Ladder_score ~ Logged_GDP_per_capita + Social_support + Healthy_life_expectancy + Freedom_to_make_life_choices + Perceptions_of_corruption" model = sm.formula.ols(formula = formula_string, data = data) model_fitted = model.fit() print(model_fitted.summary())

predicted_values = model_fitted.params.Intercept + model_fitted.params.Logged_GDP_per_capita * data['Logged_GDP_per_capita'] + model_fitted.params.Social_support * data['Social_support'] + model_fitted.params.Healthy_life_expectancy * data['Healthy_life_expectancy'] + model_fitted.params.Freedom_to_make_life_choices * data['Freedom_to_make_life_choices'] + model_fitted.params.Perceptions_of_corruption * data['Perceptions_of_corruption'] residual_scores = data['Ladder_score'] - predicted_values plt.figure(figsize=(20,20)) plt.subplot(331) sns.scatterplot(x=predicted_values, y=abs(residual_scores)) plt.title("Absolute residuals") plt.xlabel('Predicted ladder score') plt.ylabel('Residual scores') plt.subplot(332) sns.distplot(residual_scores) plt.xlabel('Residual scores') plt.title('Histogram of residual scores') plt.subplot(333) stats.probplot(x=residual_scores, plot=plt) plt.title('Q-Q plot of residual scores') plt.show() print("Figure 3: A scatter plot of the absolute residuals against the predicted ladder scores, a histogram of the residuals, and a Q-Q plot of the residuals")

plt.figure(figsize=(20,20)) plt.subplot(334) sns.scatterplot(np.arange(0, len(residual_scores)), residual_scores) plt.title('Residuals vs. order of collection') plt.xlabel('Order of collection') plt.ylabel('Residuals') plt.subplot(335) sns.scatterplot(x=data['Logged_GDP_per_capita'], y=residual_scores) plt.title('Residuals by logged GDP per capita') plt.xlabel('Logged GDP per capita') plt.ylabel('Residuals') plt.subplot(336) sns.scatterplot(x=data['Social_support'], y=residual_scores) plt.title('Residuals by social support') plt.xlabel('Social support') plt.ylabel('Residuals') plt.subplot(337) sns.scatterplot(x=data['Healthy_life_expectancy'], y=residual_scores) plt.title('Residuals by healthy life expectancy') plt.xlabel('Healthy life expectancy') plt.ylabel('Residuals') plt.subplot(338) sns.scatterplot(x=data['Freedom_to_make_life_choices'], y=residual_scores) plt.title('Residuals by freedom to make life choices') plt.xlabel('Freedom to make life choices') plt.ylabel('Residuals') plt.subplot(339) sns.scatterplot(x=data['Perceptions_of_corruption'], y=residual_scores) plt.title('Residuals by perceptions of corruption') plt.xlabel('Perception of corruption') plt.ylabel('Residuals') plt.show() print("Figure 4: Scatter plots of the residuals against the order of collection and each explanatory variable.")

explan_variables = data[['Logged_GDP_per_capita', 'Social_support', 'Healthy_life_expectancy', 'Freedom_to_make_life_choices', 'Perceptions_of_corruption']] vif = pd.DataFrame() vif['Variance Inflation Factor'] = [variance_inflation_factor(explan_variables.values, i) for i in range(explan_variables.shape[1])] vif['Features'] = explan_variables.columns print(vif)

gdp = np.corrcoef(data['Ladder_score'], data['Logged_GDP_per_capita'])[0,1] ss = np.corrcoef(data['Ladder_score'], data['Social_support'])[0,1] hle = np.corrcoef(data['Ladder_score'], data['Healthy_life_expectancy'])[0,1] ftmlc = np.corrcoef(data['Ladder_score'], data['Freedom_to_make_life_choices'])[0,1] poc = np.corrcoef(data['Ladder_score'], data['Perceptions_of_corruption'])[0,1] print('Logged GDP per capita:', gdp) print('Social support:', ss) print('Healthy life expectancy: ', hle) print('Freedom to make life choices: ', ftmlc) print('Perceptions of corruption: ', poc)

formula_string = "Ladder_score ~ Logged_GDP_per_capita" model2 = sm.formula.ols(formula = formula_string, data = data) model_fitted2 = model2.fit() print(model_fitted2.summary()) plt.figure(figsize=(8,8)) plt.scatter(x = data['Logged_GDP_per_capita'], y = data['Ladder_score']) plt.title('Ladder score vs. logged GDP per capita') plt.xlabel('Logged GDP per capita') plt.ylabel('Ladder score') sns.lineplot(x = data['Logged_GDP_per_capita'], y = model_fitted2.params.Intercept + model_fitted2.params.Logged_GDP_per_capita * data['Logged_GDP_per_capita']) plt.show() print("Figure 5: Linear regression model of the ladder score on the logged GDP per capita.")

residual_scores = data['Ladder_score'] - (model_fitted.params.Intercept + model_fitted.params.Logged_GDP_per_capita * data['Logged_GDP_per_capita']) plt.figure(figsize=(20,8)) plt.subplot(121) sns.distplot(residual_scores) plt.xlabel('Residual scores') plt.show plt.subplot(122) stats.probplot(x=residual_scores,plot=plt) plt.show() print("Figure 6: A histogram and Probability plot of the residual scores of the model of ladder score on logged GDP per capita.")