Suppose you have reason to believe that all else equal, teachers that belong to a union earn higher salaries than non-unionized teachers. To examine that possibility, you specify the following model:

,

whereis teacher salary measured in thousands of dollars, is years of teaching experience, takes the value of one if teacher i belongs to a union and zero if teacher i does not belong to a union. Using a nationally representative sample of 5,000 elementary and high school teachers, you obtain the following results with standard errors in parentheses:

1a. Interpret the coefficient on Years (mathematically and statistically).

1b. Provide a graphical illustration of the relationship between salary and years of teaching experience for both unionized and non-unionized teachers. Use a single diagram and label your diagram.

1c. Test the hypothesis that the wages of unionized teachers are different from the wages of non-unionized teachers. Use a 5% significance level for your test.

1d. Now suppose that you also had reason to believe that high school teachers earn more than elementary teachers. To examine this possibility, you specify the following model:

,

Where takes the value of unity if individual i is a high school teacher and the value of zero if individual i is an elementary teacher. You obtain the following results for this model:

Provide a graphical illustration of the relationship between salary and years of teaching experience for union/non-union teachers and for high school/elementary teachers. Use a single diagram and label your diagram.

1e. Now suppose you had reason to believe that the relationship between years of teaching experience and salary depends on union status. For example, if teachers' unions promote pay to be aligned with years of experience rather than "pay-for-performance" principles being adopted in non-union schools, you could see such variation.

What would you do to test this hypothesis? Make sure to specify a model in your answer.