Performing A Multiple Linear Regression Analysis Goal ✓ Solved

Performing a Multiple Linear Regression Analysis Goal:

Use the data set provided and the statistical methods learned in class to carry out an applied multiple linear regression analysis.

The data set for this project has been posted to Blackboard. The observational units in the sample are 146 countries. The response variable (Y) is a “HAPPY”, an index of each country’s overall happiness. Also included are 10 predictor variables (X’s), such as GDP, life expectancy, health care expenditure, and population density. The “Description” tab explains each variable.

Method: You can complete the regression using StatCrunch (recommended) or Excel:

  • StatCrunch: On MyStatLab, select “StatCrunch”, then “StatCrunch website”, then “Type or paste data into a blank data table”. Then use the “Stat” menu, “Regression”, and “Multiple Linear”. Choose the correct variables and specifications.
  • Excel: Download “Analysis ToolPak” add-in (File – Options – Add-Ins – Manage). Then “Data Analysis”, select “Regression”. Choose the correct input and specifications.

Assignment: Perform a multiple linear regression analysis. This includes:

  • List Variables: Select and list 4 predictor variables that you think may be related to happiness.
  • Explore Variables: Include a scatterplot of the response variable “HAPPY” on the y-axis and one of your predictor variables on the x-axis. Describe their relationship/correlation.
  • Write Model: Construct and write out a multiple linear regression model with your selected variables.
  • Analyze Model: Use the statistical output to identify which predictor variables are significantly important and how much of the variability in the response variable is explained (the r^2 value).
  • Finalize Model: Rerun the regression model using only the significant predictor variables. (If none were significant the first time, use the two variables with the lowest p-values.)
  • Learn from Model: Choose one variable from this finalized model and interpret its coefficient. Also, why do you think that the r^2 is so high or so low?
  • Predict with Model: Select a country from the sample. Use the values of that country’s predictor variables and the final regression model to estimate that country’s HAPPY index. Find how much the model overestimated or underestimated the true value.

Paper For Above Instructions

The goal of this project is to conduct a multiple linear regression analysis using a dataset containing happiness indices and several predictor variables for 146 countries. This analysis will allow us to explore which factors may significantly affect a country's happiness score.

Selection of Predictor Variables

After examining the dataset, I will select the following four predictor variables that I believe may have a strong correlation with the happiness index (HAPPY):

  • Gross Domestic Product per capita (GDPC)
  • Life Expectancy (DALE)
  • Health Expenditure per Capita (HLTHEXP)
  • Education Level (EDUC)

Exploring Relationships

To understand how these variables correlate with happiness, I will create a scatterplot with the HAPPY index on the y-axis and GDPC on the x-axis. Typically, we expect a direct positive correlation, indicating that higher GDP per capita contributes to greater happiness levels.

The scatterplot will illustrate points where countries with higher GDP tend to report higher happiness scores, supporting the hypothesis that economic factors influence overall well-being. Data analysis software will be utilized to generate and visualize this scatterplot accurately.

Constructing the Regression Model

The multiple linear regression model can be mathematically represented as follows:

HAPPY = β0 + β1(GDPC) + β2(DALE) + β3(HLTHEXP) + β4(EDUC) + ε

Where β0 is the intercept and β1, β2, β3, and β4 are the coefficients corresponding to each predictor variable.

Analyzing the Model

After running the multiple linear regression analysis using StatCrunch or Excel, I will summarize the statistical output to identify which predictor variables are statistically significant. Additionally, I will examine the R-squared (r²) value to determine how much variability in the happiness index is explained by the model.

A higher r² value, typically closer to 1, indicates that the model explains a large proportion of the variability in the response variable. Conversely, a lower r² value suggests a weaker model fit.

Finalizing the Model

Upon determining the significant predictors, I will rerun the regression analysis with only those variables to refine the model. If all selected variables show non-significance, I will resort to the two predictors with the lowest p-values from the initial model.

Interpreting Coefficients

From the finalized model, I will select one predictor variable and provide an interpretation of its coefficient. For instance, if the coefficient for GDPC is positive and equal to 0.25, it can be interpreted as a one-unit increase in GDP per capita leading to a 0.25 increase in the happiness index, holding all other variables constant. Understanding the significance of the coefficient helps comprehend the practical impact of each predictor on the happiness score.

The rationale behind the observed r² value will be discussed. A high r² could indicate that the chosen variables cover most factors influencing happiness, while a low r² might suggest missing external factors or measurement errors in the happiness index.

Prediction and Model Evaluation

After finalizing the regression model, I will pick a specific country, such as Sweden, and extract its predictor variable values for GDPC, DALE, HLTHEXP, and EDUC. Using these values in the final regression equation, I will predict Sweden's happiness index. Finally, I will compute the difference between the predicted value and the actual happiness index, assessing if the model accurately estimates the true value or if it demonstrates bias in overestimating or underestimating happiness.

Conclusion

Ultimately, this multiple linear regression analysis aims to identify the relationship between economic, health, and educational factors and happiness levels across countries. By understanding these relationships, policy recommendations can be made to enhance national happiness based on empirical evidence.

References

  • World Happiness Report. (2023). Sustainable Development Solutions Network.
  • United Nations Development Programme (UNDP). (2022). Human Development Reports.
  • World Health Organization (WHO). (2023). Global Health Expenditure Database.
  • OECD. (2022). OECD Health Statistics 2022.
  • International Monetary Fund (IMF). (2023). World Economic Outlook Database.
  • The World Bank. (2023). World Development Indicators.
  • StatCrunch. (2023). Online Statistics Software.
  • American Psychological Association (APA). (2022). Publication Manual of the American Psychological Association.
  • Maddison, A. (2021). The World Economy: Historical Statistics.
  • OECD. (2021). How's Life? 2021: Measuring Well-Being.

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