In a study to determine a person's yearly income 10 years after high school, it was found that the two biggest predictors are number of math and science courses taken and number of hours worked per week during a person's senior year of high school. The multiple regression equation generated from a sample of 20 individuals is
\[y^{\prime}=6000+4540 x_{1}+1290 x_{2}\]

Let \(x_{1}\) represent the number of math and science courses taken and \(x_{2}\) represent hours worked during senior year. The correlation between income and math and science courses is 0.63 . The correlation between income and hours worked is 0.84 , and the correlation between math and science courses and hours worked is 0.31 . Use this information to answer the following questions.

1. What is the dependent variable?

2. What are the independent variables?

3. What are the multiple regression assumptions?

4. Explain what 4540 and 1290 in the equation tell us.

5. What is the predicted income if a person took 8 math and science classes and worked 20 hours per week during their senior year in high school?

6. What does a multiple correlation coefficient of 0.926 mean?

7. Compute \(R^{2}\).

8. Compute the adjusted \(R^{2}\).

9. Would the equation be considered a good predictor of income?

10. What are your conclusions about the relationship among courses taken, hours worked, and yearly income?