Predicting global happiness

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.")