## Question 1: Understanding Educational Influences

**Problem Description:
**Investigate the impact of parental factors and cognitive ability on a person's years of schooling. Specifically, explore the significance of the biological father's schooling, the composite measure of cognitive ability, and the biological mother's schooling on the years of schooling.

**Table 1: Impact of parental factors vs. years of schooling
**

**Answer:** The findings reveal a significant positive impact of the biological father's schooling and cognitive ability on education. However, the influence of the biological mother's schooling is considered insignificant.

## Question 2: Assessing Model Significance and Power

**Problem Description: **Evaluate the overall significance of the model in predicting years of schooling. Additionally, analyze the power of the model based on the coefficient of determination (R^2).

**Answer: **While the model is statistically significant, the R^2 indicates a relatively low explanatory power, explaining less than half of the total variability in years of schooling.

## Question 3: Linking Education and Earnings

**Problem Description: **Examine the relationship between years of schooling and work experience on earnings. Determine the significance of these factors and the overall model in predicting earnings.

**Table 2: Relationship between years of schooling and work experience
**

**Answer:** Both schooling and work experience significantly impact earnings, as indicated by t-tests. The overall model is also statistically significant in predicting earnings.

## Question 4: Multifaceted Influences on Earnings

**Problem Description:** Investigate the joint influence of schooling, work experience, gender, and ethnicity on earnings. Determine the significance of each factor and the overall model.

**Answer:** Schooling, work experience, and gender significantly affect earnings, while ethnicity does not show a significant impact. The overall model is statistically significant.

## Question 5: Sensitivity Analysis and Model Changes

**Problem Description:** Explore how changes in reference categories affect the interpretation of coefficients and statistical tests in the model.

**Answer: **Most coefficients and statistical tests remain unchanged except for ETHHISP, and the coefficient for ETHWHITE becomes positive.

## Question 6: Regression Equation and Gender Interaction

**Problem Description: **Present a regression equation detailing the relationship between earnings, education, work experience, and gender. Investigate if there is a significant interaction effect between years of schooling and gender.

**Answer: **The overall model is statistically significant. All variables are statistically significant except ethnicity, indicating a significant interaction between years of schooling and gender.

## Question 7: Parameter Comparison

**Problem Description:** Compare parameters and test hypotheses regarding their equality or difference.

**Answer:** The null hypothesis is accepted for ASVBAR and rejected for ASVBAR vs. 2 * ASVABPC, indicating different parameter values.

## Question 8: Heteroskedasticity Test in S Dimension

**Problem Description: **Apply the Goldfeld-Quandt test to assess the presence of heteroskedasticity in the S dimension.

**Answer:** The null hypothesis of homoscedasticity is not rejected, suggesting no evidence of heteroskedasticity in the data.

## Question 9: White Test for Heteroskedasticity

**Problem Description: **Conduct the White test to investigate the presence of heteroskedasticity in the data.

**Answer:** The null hypothesis of homoscedasticity is not rejected, indicating no evidence of heteroskedasticity in the data.

## Question 10: Exogeneity Test

**Problem Description:** Assess the exogeneity of the variable ASVABC and its correlation with the error term.

**Answer: **The p-value (0.311) is greater than the significance level, indicating that ASVABC is exogenous and not correlated with the error term. The null hypothesis is not rejected.