Let's follow the steps to determine the predicted salary for an employee with 7 years of experience.
1. Identify the variables:
- Years of experience ([tex]\( x \)[/tex]): [0, 1, 2, 3, 4, 5]
- Salary ([tex]\( y \)[/tex]) in dollars: [40000, 42150, 44260, 46785, 48820, 51126]
2. Determine the equation of the line of best fit:
The line of best fit can be described by the equation [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
3. Calculate the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( b \)[/tex]) of the line:
- Slope [tex]\( m = 2233.29 \)[/tex]
- Y-intercept [tex]\( b = 39940.29 \)[/tex]
4. Formulate the linear equation for the line of best fit:
- The equation derived from the data is [tex]\( y = 2233.29x + 39940.29 \)[/tex]
5. Predict the salary for 7 years of experience:
- Let [tex]\( x = 7 \)[/tex]
- Substitute [tex]\( x = 7 \)[/tex] into the equation [tex]\( y = 2233.29x + 39940.29 \)[/tex]
[tex]\[
y = 2233.29 \times 7 + 39940.29
\][/tex]
6. Calculate the predicted salary:
[tex]\[
y = 2233.29 \times 7 + 39940.29
\][/tex]
[tex]\[
y = 15632.99 + 39940.29
\][/tex]
[tex]\[
y = 55573
\][/tex]
7. Round the predicted salary to the nearest dollar:
- The predicted salary for an employee with 7 years of experience is [tex]\( \$55,573 \)[/tex].
So, the correct answer is:
- [tex]\(\$ 55,573\)[/tex]
