How to Approach Happiness Score Prediction in Predictive Modelling Assignments

Typical Goal Example:

• Predict the dependent variable (Y) — e.g., a happiness score.
• Exclude specific predictors (e.g., "Dystopia," "upperwhisker," "lowerwhisker").
• Achieve model performance better than benchmark values like:
  • Adjusted R² ≥ 0.89
  • AIC ≤ 95
  • BIC ≤ 117

Key theoretical skills involved:

• Variable selection and transformation
• Model comparison using AIC, BIC, and F-tests
• Diagnostic checking of residuals
• Interval estimation and interpretation
• Outlier and influence analysis

2. Initial Data Exploration and Cleaning

Before jumping into modeling, it’s essential to understand your variables:

• Identify the outcome variable (typically a happiness index).
• Scan for missing values, outliers, and inconsistencies.
• Standardize or normalize variables if needed, especially if some predictors are on vastly different scales.

Although transformations are not always required, checking for skewed distributions and potential nonlinear relationships can guide decisions on whether log or square-root transformations might improve linearity and homoscedasticity.

3. Choosing Candidate Predictors

Students often feel tempted to use every variable in the dataset. However, these assignments emphasize thoughtful exclusion (e.g., "do not use Dystopia").

Key techniques for predictor selection:

• Theoretical grounding: Choose predictors that logically influence happiness (e.g., income, life expectancy, corruption perceptions).
• Correlation analysis: Examine pairwise correlations with the dependent variable.
• Avoid multicollinearity: Use Variance Inflation Factor (VIF) to avoid redundant variables.

Note: You may be asked to “break into two parts,” which implies exploring whether segmented or piecewise regression models provide better fit or interpretability.

4. Model Building Strategy

Students should aim for a systematic model-building approach rather than trial-and-error. A solid strategy includes:

• Forward selection: Start with no predictors and add one at a time.
• Backward elimination: Start with all and remove the least significant iteratively.
• Stepwise regression: Combines forward and backward strategies.
• Regularization (if allowed): Techniques like LASSO or Ridge regression can help if multicollinearity is a concern.

Most assignments prohibit the use of automated software for feature selection, so students should justify each inclusion.

5. Evaluating the Final Model

Once a final model is selected, it must be justified against alternatives.

Comparison metrics:

• Adjusted R²: Corrects for the number of predictors.
• AIC and BIC: Penalize model complexity to prevent overfitting.

Equation (1): Adjusted R²

Adjusted R2=1−((1−R2)(n−1)n−k−1)\text{Adjusted } R^2 = 1 - \left(\frac{(1 - R^2)(n - 1)}{n - k - 1}\right)

Where:

• n = sample size
• k = number of predictors

A good model will meet or exceed the given benchmarks. But meeting them is not enough—the model’s interpretability, residual behavior, and predictive accuracy also matter.

6. Model Comparison Using F-Test

Assignments often require students to use an F-test to determine whether a more complex model significantly improves fit.

Equation (2): F-statistic

F=(RSS1−RSS2)/(df1−df2)RSS2/df2F = \frac{(RSS_1 - RSS_2) / (df_1 - df_2)}{RSS_2 / df_2}

Where:

• RSS = residual sum of squares
• df = degrees of freedom for the models

The F-test compares nested models. If your final model performs significantly better than the penultimate one, it strengthens your case.

7. Residual Diagnostics

No model is complete without checking its assumptions:

• Linearity: Relationship between predictors and outcome should be linear.
• Homoscedasticity: Residuals should have constant variance.
• Normality: Residuals should be normally distributed.
• Independence: Residuals should not be autocorrelated (less of an issue with country-level data).

Tools for checking:

• Residual vs Fitted plot
• Q-Q plot for normality
• Scale-Location plot
• Histogram of residuals
• Shapiro-Wilk test (optional, if plots look questionable)

If these diagnostics raise red flags, transformations or robust regression methods might be required.

8. Confidence and Prediction Intervals

Once the model is validated, construct and interpret intervals:

• Confidence interval for slope: Reflects uncertainty in the coefficient estimate.
• Prediction interval: Gives a range where future observations (e.g., a withheld country like Latvia) are expected to fall.

Equation (3): Confidence Interval for Slope

β±tn−k⋅SE(β)\beta \pm t_{n-k} \cdot SE(\beta)

Assignments may ask whether the true value (e.g., Latvia’s score) lies within the prediction interval and if model assumptions impact this result.

9. Outliers and Influential Observations

Two statistical tools help identify problematic data points:

• Studentized residuals: Identify outliers. Threshold: |r_i| > 2 or 3 (more stringent under Bonferroni correction)
• Cook’s Distance & Leverage: Measure influence. High leverage + large residual → high influence

A good modeler explains not only which countries are influential but also why—e.g., unusual GDP, extreme social scores, or data anomalies.

10. Explaining the Findings Simply

Some assignments require presenting the model’s insights to a general audience. Here’s how to translate statistical results into accessible ideas:

“We found that countries with higher social support, longer life expectancy, and less corruption tend to be happier. But wealth alone doesn’t guarantee happiness—how people feel supported matters just as much!”

This final slide tests a student’s ability to extract meaning, not just data. It’s also a great way to demonstrate communication skills essential for data science and policy roles.

Conclusion

Predictive modeling assignments involving happiness scores require more than statistical computation—they demand strategy, diagnostics, communication, and interpretation. By following a structured approach that includes thoughtful variable selection, robust model diagnostics, and clear reporting, students can craft solutions that not only meet quantitative benchmarks but also deliver valuable insights.

Whether you're working with happiness data or another national index, the principles remain consistent: understand the data, test your models rigorously, and ensure your conclusions are supported both statistically and conceptually.

If you're tackling a similar assignment and feeling overwhelmed, our platform offers expert help tailored to statistics assignments of this nature. From understanding variable relationships to ensuring your model beats the instructor’s benchmark, we’re here to support your academic success.