# Multivariate Regression Analysis and Hypothesis Testing Skills in Excel

This comprehensive presentation delves into various aspects of Multivariate Regression Analysis and Hypothesis Testing assignment using Excel and emphasizing the application of these skills. From understanding educational influences and assessing model significance to examining the complex interplay of factors influencing earnings, each question is tackled systematically. The detailed answers showcase proficiency in Excel, demonstrating regression equations, sensitivity analyses, and statistical tests. This content provides a thorough exploration of analytical skills, showcasing the application of Excel as a powerful tool for statistical modeling and hypothesis testing in a multivariate context.

## 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.