The dataset for this week ( https://www.kaggle.com/datasets/eliasturk/world-happiness-based-on-cpi-20152020) and using only the interval level or above variables, in JASP perform ONLY ONE variable selection process

Sample Solution

Results of Variable Selection in World Happiness Dataset

This analysis explores variable selection methods using the World Happiness Report dataset (https://www.kaggle.com/datasets/eliasturk/world-happiness-based-on-cpi-20152020), focusing on interval or above level variables. We will perform only one variable selection process and report the final three regression tables.

Method: Forward Selection

Reasoning:

This approach iteratively adds the most significant predictor to the model at each step. It starts with an empty model and considers all available variables. The variable with the strongest association with the dependent variable (happiness score) is added first. Then, the remaining variables are evaluated based on their contribution to the model when added alongside the already selected variables. This process continues until no remaining variable adds statistically significant improvement to the model's explanatory power.

Strength of Forward Selection:

• Relatively easy to understand and interpret.
• Provides a sequential view of how variables contribute to the model.

Weakness of Forward Selection:

• May not reach the absolute "best" model compared to some other methods (e.g., stepwise selection).

Final Regression Tables:

Unfortunately, JASP output cannot be directly embedded here. However, I can describe the steps involved in obtaining the final three regression tables using Forward Selection in JASP:

Full Answer Section

Step 1: Initial Model

1. Import the "WorldHappiness_Corruption_2015_2020.csv" dataset into JASP.
2. Select "Linear Regression" from the "Analyze" menu.
3. Set "Happiness Score" as the dependent variable.
4. In the "Independent Variables" section, use the dropdown menu to select the "Forward Selection" method.
5. Click "Run" to perform the initial model with no predictors.

Step 2 & 3: Adding Significant Predictors

JASP will automatically perform the forward selection process. It will display a series of tables:

• The first table shows the initial model with no predictors and baseline statistics.
• Subsequent tables will add the most significant variable based on the chosen criteria (usually p-value). Each table will display:
  • Adjusted R-squared value indicating the model's explanatory power after considering model complexity.
  • F-statistic and its significance level to assess the overall model fit.
  • Individual coefficient estimates for each variable in the model, along with their standard errors and p-values.

You can stop the selection process after the third table if it shows a significant improvement in fit (high adjusted R-squared, low p-value for F-statistic) and includes variables relevant to your research question.

Final Regression Equation:

Based on the final regression table, you can extract the regression equation. This equation will include the intercept (constant term) and coefficients for each of the selected predictor variables. The equation will look something like this:

Happiness Score = β₀ + β₁Variable₁ + β₂Variable₂ + ... + ε

where:

• β₀ is the intercept (constant term)
• β₁ to βₙ are the coefficients for each selected predictor variable
• ε represents the error term

By analyzing these final three regression tables and the final regression equation, you can gain insights into which interval or above level variables have the most significant impact on happiness scores in this dataset, based on the chosen forward selection method.