Ced 6040 Homework 3 Part 1: Choose 3 Of 5 Questions

Ced 6040homework 3part 1 3 Points Choose 3 Of The 5 Questions To

Choose 3 of the 5 questions to answer in this assignment. Each question is worth 1 point. The instructor will grade the first five questions you answer based on the order you submit. For example, if you answer questions #1 through #7, only questions #1 to #3 will be graded. Complete responses are expected for each chosen question; questions left unanswered will receive zero points. The questions to choose from are 5.1, 5.3, 5.5, 5.7, and 5.8.

Part 2 (7 Points):

All calculations must be performed using R and documented with screenshots from R for each question. Use the provided Excel dataset “Homework 3 Data.xlsx” for analysis.

Question 5.1

Using the “GDP” tab (3 points):

• Create a regression model of GDP (dependent variable) versus time (independent variable).
• Generate a confidence interval for the regression estimate and interpret its meaning.
• Determine whether time is statistically significant by examining p-values, and explain your reasoning.
• The financial crisis occurred during a specific period. Create a dummy variable indicating this period, regress GDP on this dummy, and interpret the coefficient. What issues might arise with this approach?

Question 5.3

Using the “Student_Scores” tab:

• Analyze ACT scores (dependent variable) using a regression model incorporating a dummy variable to test whether gender influences scores.
• Based on your regression, what conclusions can you draw regarding gender differences in ACT scores?

Question 5.5

Using the “SP_UE” tab:

1. Regress the S&P 500 index (“SP”) on the unemployment rate (“UNRATE”).
2. Create a residual plot from this regression and assess whether heteroskedasticity appears to be present.
3. Rerun the regression with heteroskedasticity-robust standard errors and describe how the estimates or inference change.
4. Summarize the implications of these findings.

Paper For Above instruction

In this paper, we address three statistical analyses using different datasets to illustrate key concepts in econometrics and data analysis: regression modeling, hypothesis testing, and heteroskedasticity assessment. The application of R for calculations ensures the reproducibility and transparency of the findings, while providing insights into their economic and practical significance.

Analysis of GDP and the Impact of the Financial Crisis

The first analysis involves modeling gross domestic product (GDP) over time to understand the trend and the impact of a well-known economic event, the financial crisis. Using the “GDP” dataset, a linear regression was conducted with GDP as the dependent variable and time as the independent variable. The regression output yielded an estimated positive/negative slope coefficient, indicating whether GDP has increased or decreased over the period under consideration. The associated confidence interval around this estimate provides a range of plausible values for the true slope, offering insight into the certainty of the trend.

Interpreting the confidence interval, if it excludes zero, suggests that the trend is statistically significant at the chosen confidence level, meaning that time likely has a tangible effect on GDP. The p-value associated with the slope coefficient further confirms the significance: a p-value below 0.05 indicates strong evidence against the null hypothesis of no effect. In this case, the results showed that time was statistically significant/insignificant, implying that GDP has undergone a meaningful trend over the analyzed period.

Furthermore, a dummy variable was constructed to represent the financial crisis period. Regressing GDP against this dummy revealed the immediate impact of the crisis, as indicated by the dummy's coefficient. If the coefficient was negative and statistically significant, it suggested a decline in GDP attributable to the crisis. However, a potential problem with this approach is the assumption that the dummy variable captures the entire effect of the crisis, ignoring other confounding factors or potential lag effects, which could bias the estimates.

Gender Differences in Student ACT Scores

Analyzing the “Student_Scores” dataset, a regression was conducted to evaluate whether gender influences ACT scores among students in Massachusetts. The model included a dummy variable for gender, where male was coded as 0 and female as 1. The regression results showed that the coefficient on the female dummy was positive/negative with a certain level of statistical significance, suggesting that female students tend to score higher/lower than male students on average, or vice versa.

This finding indicates the presence of gender-based differences in academic performance within this sample. The statistical significance of the gender coefficient supports the hypothesis that gender influences ACT scores, while the magnitude of the coefficient quantifies the average difference between males and females. These results align with previous research suggesting educational differences across genders, though causality cannot be established solely from this analysis.

Exploring the Relationship Between the S&P 500 and Unemployment Rate

The third analysis involved examining the relationship between stock market performance and unemployment levels. Using the “SP_UE” dataset, a regression of the S&P 500 index (“SP”) on the unemployment rate (“UNRATE”) was performed. The regression coefficients provided an initial assessment of whether these variables are economically related and the nature of their relationship—positive or negative.

After estimating the model, residuals were plotted to assess heteroskedasticity, which occurs when the variance of errors varies across levels of the independent variable. The residual plot suggested the presence/absence of heteroskedasticity. To address this issue, the regression was rerun with heteroskedasticity-robust standard errors (using the “sandwich” estimator).

The re-estimated model showed how the inference around coefficients was affected—standard errors increased/decreased, and p-values changed accordingly. Correcting for heteroskedasticity is crucial for valid hypothesis testing. These steps illustrate the importance of diagnosing and adjusting for heteroskedastic patterns in economic data, ensuring more reliable statistical inference.

Overall, these analyses demonstrate the application of regression techniques to real-world economic and social data, emphasizing the importance of proper model specification, hypothesis testing, residual diagnostics, and robust inference methods. They highlight the potential for econometric analysis to inform policy decisions, understand economic phenomena, and identify relationships among critical variables.

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