To determine the estimated annual salary for the employee, follow these steps:
1. Identify the base salary and coefficients:
- Base salary (intercept): [tex]\(11.507 + 0.30\)[/tex]
- Education coefficient: [tex]\(3258.45\)[/tex]
- Experience coefficient: [tex]\(811.24\)[/tex]
2. Determine the employee's years of education and work experience:
- Years of education after the 8th grade = 10 years (which translates to a total of 18 years of education).
- Years of experience with the company = 12 years.
3. Apply the values to the regression model formula:
The regression model formula is:
[tex]\[
\text{Estimated Salary} = \text{Base Salary} + (\text{Education Coefficient} \times \text{Years of Education}) + (\text{Experience Coefficient} \times \text{Years of Experience})
\][/tex]
Plugging in the values:
[tex]\[
\text{Base Salary} = 11.507 + 0.30
\][/tex]
[tex]\[
\text{Base Salary} = 11.807
\][/tex]
4. Plug the values into the regression formula with the coefficients and years:
[tex]\[
\text{Estimated Salary} = 11.807 + (3258.45 \times 10) + (811.24 \times 12)
\][/tex]
5. Calculate the contribution from education:
[tex]\[
3258.45 \times 10 = 32584.50
\][/tex]
6. Calculate the contribution from experience:
[tex]\[
811.24 \times 12 = 9734.88
\][/tex]
7. Add all the terms to get the estimated annual salary:
[tex]\[
\text{Estimated Salary} = 11.807 + 32584.50 + 9734.88
\][/tex]
[tex]\[
\text{Estimated Salary} = 42331.187
\][/tex]
Therefore, the estimated annual salary for the employee is [tex]\(\$42,331.19\)[/tex] (rounded to two decimal places).
