Basic Econometrics Individual Assignment

1. Use R to run the following cross-sectional regression. (Please note the natural logs and construct these in R as needed):

Lifeexp=β0+β1log(GDPpc)+β2Electricity+β3Sanitation+β4Sanitation2+β5Education+β6Immunization+u

(Equation 1)

• Present your regression results in a table below (copy and paste R output):
• Interpret the constant (intercept) (2.5 marks) and its p-value (1.5 marks).
• Interpret the coefficient on GDP per capita (2.5 marks) and its p-value (1.5 marks).
• Calculate the turning point of the quadratic relationship (2 marks) and interpret the result (2 marks). Is the relationship U-shaped or inverted U shaped? Draw a scatter plot of the relationship between life expectancy and sanitation. Is this a significant relationship? (1 mark)
• Interpret the coefficient on Access to Electricity (% of population) (2.5 marks) and its p-value (1.5 marks).
• Interpret the coefficient Immunization, HepB3 (% of one-year-old children) and show the calculation of its t-stat. Interpret the calculated t-statistic (2 marks each).
• Interpret the R2 of the regression.
• Several explanatory variables would be in a multicollinear relationship with each other. Explain perfect and imperfect multicollinearity and present a correlation matrix between the independent variables in Equation 1.

2. Specify if the 5 Gauss-Markov assumptions are likely to hold for the regression in Question 1 or not and explain why each assumption holds or not holds (no formal test is required).

3. Run the following regression

log(Lifeexp)=β0+β1log(GDPpc)+β2Electricity+β3Sanitation+β4Sanitation2+β5Education+β6Immunization+u

• Present your regression results in a table below (copy and paste R output):
• Interpret the coefficients for log(GDPpc) and Electricity (2.5 marks each)
• Would you use Model 1 or Model 2 if you had a choice? Justify your choice.
• Present a functioning R code (copy and paste here) reproducing the results. This is a critical part of the assignment without which we’ll initiate a plagiarism check.

4. Present a functioning R code (copy and paste here) reproducing the results. This is a critical part of the assignment without which we’ll initiate a plagiarism check.

Summary of Assessment Requirements

This individual assignment required students to apply econometric analysis using R programming. The key tasks included:

1. Cross-sectional regression analysis

   • Estimate the regression:Lifeexp=β0+β1log⁡(GDPpc)+β2Electricity+β3Sanitation+β4Sanitation2+β5Education+β6Immunization+uLifeexp = β0 + β1 \log(GDPpc) + β2 Electricity + β3 Sanitation + β4 Sanitation^2 + β5 Education + β6 Immunization + uLifeexp=β0+β1log(GDPpc)+β2Electricity+β3Sanitation+β4Sanitation2+β5Education+β6Immunization+u
   • Present regression results in a table and interpret coefficients, p-values, constant term, and the quadratic relationship (including turning point).
   • Generate and interpret a scatter plot of life expectancy vs. sanitation.
   • Discuss the statistical significance of the relationships.
   • Calculate and interpret the t-stat for immunization.
   • Interpret the R⊃2; of the regression.
   • Explain multicollinearity (perfect vs. imperfect) and present a correlation matrix.

2. Gauss-Markov assumptions

   • Evaluate whether each of the five assumptions holds for the regression and justify the reasoning.

3. Alternative regression specification

   • Estimate the model using log(Lifeexp) as the dependent variable.

   • Present regression results, interpret selected coefficients, and justify whether Model 1 or Model 2 is preferable.

4. R code submission

   • Provide functioning R code for all regression outputs, scatter plots, and correlation matrices. This was mandatory to demonstrate originality and reproducibility.

Step-by-Step Approach Guided by the Academic Mentor

The mentor guided the student systematically through the assignment:

Step 1: Setting up the regression (Question 1)

• Explained how to prepare the dataset in R and construct log-transformed variables where required.
• Guided on running the regression using lm() and formatting results into a readable table.
• Walked through the interpretation of the constant and coefficients, emphasizing the meaning of p-values in determining significance.
• Clarified the quadratic term for sanitation, showing how to compute the turning point and interpret whether the relationship was U-shaped or inverted U-shaped.
• Demonstrated scatter plot creation in R (ggplot2 or plot()) and guided on linking visualization with regression findings.

Step 2: Statistical interpretation

• Mentored on calculating a t-statistic manually from regression output and cross-checking it against the R output.
• Explained the interpretation of R⊃2; as a goodness-of-fit measure in cross-sectional regressions.
• Introduced multicollinearity, helping the student differentiate between perfect and imperfect cases, and showing how to create and interpret a correlation matrix in R.

Step 3: Gauss-Markov assumptions (Question 2)

• Encouraged critical evaluation of each assumption (linearity, random sampling, no perfect multicollinearity, zero conditional mean, homoskedasticity).
• Explained practical reasoning (e.g., why independence may be questionable in cross-country data, or why heteroskedasticity might occur in socio-economic variables).

Step 4: Alternative specification (Question 3)

• Demonstrated how to rerun the regression with log(Lifeexp) and interpret the elasticity form of coefficients.
• Encouraged comparison of both models (levels vs. logs), considering interpretability, model fit, and statistical robustness.
• Discussed criteria for model selection.

Step 5: R code (Question 4)

• Ensured the student compiled all R scripts, annotated them properly, and tested outputs for reproducibility.
• Reinforced academic integrity by stressing the importance of including functioning code to avoid plagiarism concerns.

Outcome and Learning Objectives Covered

By the end of the assignment, the student was able to:

• Apply econometric methods in R to real-world socio-economic data.
• Interpret regression coefficients, p-values, and statistical relationships in context.
• Understand and apply quadratic relationships and their real-world implications.
• Generate and interpret correlation matrices to identify multicollinearity issues.
• Critically evaluate econometric assumptions under the Gauss-Markov framework.
• Compare model specifications and justify choices based on statistical and practical reasoning.
• Develop reproducible R code, reinforcing transparency and good research practice.

The mentor’s structured guidance ensured that the student not only completed the assignment successfully but also gained confidence in econometric analysis, statistical interpretation, and technical coding skills.

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