Regression Part 3

Lecture by Tamar Kugler, Associate Professor of Management and Organizations at the University of Arizona Eller MBA.

Regression analysis helps to establish relationships between various variables.
Focus is given to predicting salary based on different independent factors using regression models.

Scatter Plot: Illustrates the relationship between rating (x-axis) and salary (y-axis).
- Rating scale: 2 to 9 (no data for a rating of 1).
- Displays a positive trend indicating a relationship.
R-Square Value: R^2 = 0.71
- Represents that 71% of the variance in salary can be explained by the rating.
- Compared to previous findings (minority status R-square = 0.086).
- Indicates a strong predictive capability of ratings on salary.
Adjusted R-Square: Almost unchanged due to a favorable ratio of observations (n = 140) to predictors (one predictor).
Regression Equation:
- \text{Predicted Salary} = 636 + 151 \times \text{Rating}
- Interpretation of intercept (636): This value represents an average score for a theoretical rating of 0, which doesn’t exist in this model.
- Slope Interpretation: For each unit increase in rating, salary increases by 151.
Statistical Significance:
- T-statistic = 18.5, suggesting it's significantly greater than zero.
- P-value = 2.28 \times 10^{-39}, effectively zero.
- Conclusion: There is a significant relationship, and the effect of rating on salary is statistically proven.

Scatter Plot: Indicates no significant relationship between age and salary, displaying a flat regression line.
R-Square Value: R^2 = 0.009
- Less than 1% of salary variance can be attributed to age.
Coefficient Interpretation:
- Coefficient for age: 7.2; suggests an increase of 7 in salary for each additional year of age.
- Statistical Significance: P-value = 0.26, indicating a lack of significance (greater than alpha level of 0.05).
- Conclusion: No significant relationship found between age and salary.

Scatter Plot: Illustrates minimal spread around two gender categories (0 for women, 1 for men).
- Regression line remains flat, indicating no relationship.
R-Square Value: Very close to zero.
Coefficient Interpretation:
- Coefficient for gender: approximately 11, suggesting men earn 11 more than women on average.
- Statistical Significance: P-value = 0.88; therefore, can be treated as zero.
- Conclusion: There is no significant evidence that gender impacts salary in this organization.

Scatter Plot: Positive relationship observed between tenure (in years) and rating, upward trending regression line.
R-Square Value: R^2 = 0.73
- This indicates that 73% of the variance in rating can be explained by tenure.
Regression Equation:
- \text{Predicted Rating} = 0.86 + 1.78 \times \text{Tenure}
- Interpretation: Each additional year of tenure increases the rating by approximately 1.78 points, which is significant as ratings range from 1 to 9.
Statistical Significance:
- P-value = 1.98 \times 10^{-41}, which is significantly lower than alpha.
- Conclusion: We reject the null hypothesis and conclude tenure significantly impacts rating.

Significant effects are observed:
- Minority status affecting salary.
- Rating score significantly predicts salary.
- Tenure positively correlates with ratings.
No significant effect observed from age or gender on salary.
Need for further analysis to control for confounding factors affecting salary, including performance evaluation ratings and tenure.
Upcoming discussion will include extending the regression model to include multiple predictors simultaneously for a more comprehensive analysis.